Is this supported?  We're using the Twitter app, and I wrote a schedulable class that calls the AutomationWrapper included in this package to update our conversations every ten minutes.  The code in my class executes on its own as expected, but when it's run via the scheduler, it appears that the HTTP callouts are simply skipped.

This is the log.  This code takes an absolute minimum of 2 full seconds to execute when working properly.  When run from the scheduler, its' done in less than 300ms, which leads me to believe that the HTTP callouts are just being skipped.

18.0 APEX_CODE,DEBUG;APEX_PROFILING,INFO;CALLOUT,INFO;DB,INFO;VALIDATION,INFO;WORKFLOW,INFO1:30:0.26|EXECUTION_STARTED1:30:0.26|CODE_UNIT_STARTED|[EXTERNAL]Twitter Synch 41:30:0.41|SOQL_EXECUTE_BEGIN|[4,40]|Aggregations:0|select id from sf4twitter__twitter_account__c where name = 'logmeinhelp' limit 11:30:0.48|SOQL_EXECUTE_END|[4,40]|Rows:1|Duration:71:30:0.49|METHOD_ENTRY|[5,14]|sf4twitter.AutomationWrapper.doSearchAccount(Id, Integer)1:30:0.49|ENTERING_MANAGED_PKG|sf4twitter1:30:0.49|SOQL_EXECUTE_BEGIN|[116,42]|Aggregations:0| Select t.Username__c, t.Unknown_Twitter_Usernames__c, t.Twitter_User_Id__c, t.Twitter_Max_Twitter__c, t.Twitter_Max_Message__c, t.SystemModstamp, t.Password__c, t.OwnerId, t.Name, t.LastModifiedDate, t.LastModifiedById, t.IsDeleted, t.Id, t.Enable_Auto_Case_Creation__c, t.CreatedDate, t.CreatedById, t.Bit_ly_Username__c, t.Bit_ly_Password__c, associate_DM__c , ignore_maxid__c, closed_case_duration__c From Twitter_Account__c t Where Id =:taId 1:30:0.58|SOQL_EXECUTE_END|[116,42]|Rows:1|Duration:91:30:0.59|SOQL_EXECUTE_BEGIN|[27,34]|Aggregations:0|select id, name from Account where name = :Label.TWITTER_ACCOUNT_NAME1:30:0.114|SOQL_EXECUTE_END|[27,34]|Rows:0|Duration:551:30:0.115|SOQL_EXECUTE_BEGIN|[60,21]|Aggregations:0|Select Name, Id, OwnerId, Username__c, Unknown_Twitter_Usernames__c, Password__c, Twitter_Max_Message__c, Enable_Auto_Case_Creation__c, Bit_ly_Username__c, Bit_ly_Password__c, Twitter_Max_Twitter__c, associate_DM__c, associate_cases_same_username__c, closed_case_duration__c From Twitter_Account__c LIMIT 10001:30:0.118|SOQL_EXECUTE_END|[60,21]|Rows:2|Duration:31:30:0.132|SOQL_EXECUTE_BEGIN|[156,17]|Aggregations:0|select id, twitterId__c from Case where twitterId__c in :tids1:30:0.136|SOQL_EXECUTE_END|[156,17]|Rows:0|Duration:41:30:0.139|SOQL_EXECUTE_BEGIN|[399,20]|Aggregations:0|select id, twitter_username__c from Contact where twitter_username__c in :twitterUserNames LIMIT 10001:30:0.142|SOQL_EXECUTE_END|[399,20]|Rows:0|Duration:31:30:0.142|SOQL_EXECUTE_BEGIN|[402,17]|Aggregations:0|select id, twitter_username__c from Lead where IsConverted = false and twitter_username__c in :twitterUserNames LIMIT 10001:30:0.153|SOQL_EXECUTE_END|[402,17]|Rows:0|Duration:111:30:0.153|SOQL_EXECUTE_BEGIN|[361,18]|Aggregations:0|Select Id, twitterID__c, ContactId, Twitter_Username__c from Case where twitterID__c in :twitterIds1:30:0.155|SOQL_EXECUTE_END|[361,18]|Rows:0|Duration:21:30:0.156|SOQL_EXECUTE_BEGIN|[366,40]|Aggregations:0|select Id, Case__c, Case__r.ClosedDate, Case__r.Status, Contact__c, twitterid__c, Parent__c, type__c from Twitter_Conversation__c where twitterid__c in :twitterIds LIMIT 10001:30:0.164|SOQL_EXECUTE_END|[366,40]|Rows:0|Duration:81:30:0.164|SOQL_EXECUTE_BEGIN|[371,40]|Aggregations:0|select Id, Case__c, Case__r.ClosedDate, Case__r.Status, Contact__c, twitterid__c, Parent__c, Content__c, Author_Real_Name__c, Author_Name__c, type__c, In_Reply_To_Status_Id__c, In_Reply_To_User_Id__c from Twitter_Conversation__c where twitterid__c in :twitterReply LIMIT 10001:30:0.168|SOQL_EXECUTE_END|[371,40]|Rows:0|Duration:41:30:0.171|SOQL_EXECUTE_BEGIN|[663,18]|Aggregations:0|select id, twitterId__c, Twitter_Username__c, CreatedDate, ContactId, Contact.Twitter_Username__c from Case where ((Status != :Label.TWITTER_CASE_CLOSED or ClosedDate >= :closeDuration) and Twitter_Username__c IN :fromUsernames) or Id IN :repCasesId order by LastModifiedDate desc LIMIT 10001:30:0.181|SOQL_EXECUTE_END|[663,18]|Rows:0|Duration:101:30:0.181|SOQL_EXECUTE_BEGIN|[677,40]|Aggregations:0|select id, Content__c,Case__c, Parent__c, Author_Name__c from Twitter_Conversation__c where Case__c IN :casesIds LIMIT 10001:30:0.183|SOQL_EXECUTE_END|[677,40]|Rows:0|Duration:21:30:0.183|SOQL_EXECUTE_BEGIN|[705,36]|Aggregations:0|select In_Reply_To_Status_Id__c, id, Case__r.Status, Case__r.twitterId__c, Case__r.Twitter_Username__c, Case__r.CreatedDate, Case__r.ContactId, Author_Name__c from Twitter_Conversation__c where (In_Reply_To_Status_Id__c in :repliedRAStatusTwitterIds) and (Case__r.Status != :Label.TWITTER_CASE_CLOSED or Case__r.ClosedDate >= :closeDuration) order by Case__r.LastModifiedDate desc limit 10001:30:0.187|SOQL_EXECUTE_END|[705,36]|Rows:0|Duration:41:30:0.188|DML_BEGIN|[621,42]|Op:Upsert|Type:Case|Rows:01:30:0.188|DML_END|[621,42]|1:30:0.190|SOQL_EXECUTE_BEGIN|[561,20]|Aggregations:0|select id, twitter_username__c from Contact where twitter_username__c in :twitterUserNames LIMIT 10001:30:0.192|SOQL_EXECUTE_END|[561,20]|Rows:0|Duration:21:30:0.192|DML_BEGIN|[583,42]|Op:Upsert|Type:Case|Rows:01:30:0.193|DML_END|[583,42]|1:30:0.193|SOQL_EXECUTE_BEGIN|[411,42]|Aggregations:0|select TwitterID__c, Twitter_Account__c, Direct_Message__c,type__c from Twitter_Conversation__c where Type__c = :Label.TWITTER_TYPE_REPLIES and Twitter_Account__c in :accounts.keySet() order by TwitterID__c desc limit 11:30:0.201|SOQL_EXECUTE_END|[411,42]|Rows:1|Duration:81:30:0.201|SOQL_EXECUTE_BEGIN|[414,51]|Aggregations:0|select TwitterID__c, Twitter_Account__c, Direct_Message__c,type__c from Twitter_Conversation__c where Type__c = :Label.TWITTER_OUTBOUND_DIRECTMESSAGE and Twitter_Account__c in :accounts.keySet() and Direct_Message__c != null order by TwitterID__c desc limit 11:30:0.205|SOQL_EXECUTE_END|[414,51]|Rows:0|Duration:41:30:0.205|SOQL_EXECUTE_BEGIN|[418,45]|Aggregations:0|select TwitterID__c, Twitter_Account__c, Direct_Message__c,type__c from Twitter_Conversation__c where (Type__c = :Label.TWITTER_TYPE_REGISTERED_ACCOUNT or Type__c = :Label.TWITTER_OUTBOUND_REPLY) and Twitter_Account__c in :accounts.keySet() and Direct_Message__c = null order by TwitterID__c desc limit 11:30:0.211|SOQL_EXECUTE_END|[418,45]|Rows:1|Duration:61:30:0.211|SOQL_EXECUTE_BEGIN|[422,41]|Aggregations:0|select TwitterID__c, Twitter_Account__c, Direct_Message__c,type__c from Twitter_Conversation__c where Type__c = :Label.TWITTER_TYPE_DIRECT_MESSAGE and Twitter_Account__c in :accounts.keySet() order by TwitterID__c desc limit 11:30:0.215|SOQL_EXECUTE_END|[422,41]|Rows:0|Duration:41:30:0.218|DML_BEGIN|[443,3]|Op:Update|Type:sf4twitter__Twitter_Account__c|Rows:11:30:0.238|ENTERING_MANAGED_PKG|sf4twitter1:30:0.238|SOQL_EXECUTE_BEGIN|[5,42]|Aggregations:0|select id, Username__c from Twitter_Account__c where Username__c =: Trigger.new[0].Username__c and ownerId = :UserInfo.getUserId()1:30:0.243|SOQL_EXECUTE_END|[5,42]|Rows:1|Duration:51:30:0.243|CUMULATIVE_LIMIT_USAGE1:30:0.243|CUMULATIVE_LIMIT_USAGE_END1:30:0.256|DML_END|[443,3]|1:30:0.257|METHOD_EXIT|[5,14]|doSearchAccount(Id, Integer)1:30:0.257|METHOD_ENTRY|[6,3]|system.debug(String)1:30:0.258|USER_DEBUG|[6,3]|DEBUG|result: <?xml version="1.0" encoding="UTF-8"?><result><conversations>0</conversations><cases>0</cases><caseComments>0</caseComments><contacts>0</contacts><leads>0</leads><errorCode>null</errorCode><errorMsg>null</errorMsg><pageNumber>0</pageNumber></result>1:30:0.258|METHOD_EXIT|[6,3]|debug(ANY)1:30:0.258|CODE_UNIT_FINISHED1:30:0.258|EXECUTION_FINISHED

 The scheduler class that I'm running every 10 minutes

global class SynchTwitter Implements Schedulable{ global void Execute(SchedulableContext SC){ sf4twitter__twitter_account__c acc = [select id from sf4twitter__twitter_account__c where name = 'mytwitteraccountname' limit 1]; string s = sf4twitter.automationwrapper.doSearchAccount(acc.id,0); system.debug('result: ' + s); }}

 I let this run for an hour, and no results were ever pulled back.  I ran the code inside the execute method on its own via the system log window, and it pulled back the conversations I was expected to be pulled.

The documentation for the Spring '10 release does not indicate that HTTP callouts are not supported in Scheduled Apex.  I'm not willing to write a complete class just to confirm whether or not it's supported, and I can't see any issues with the Twitter class debug log (it's a managed package, so I can't see what's being done where). 

Please advise.