No You have made a mistake in your code, the param you are passing should be assigned to any property ( property has to be public) in the controller. See this example

/*** Controller ***/
public class exampleCon {
String uname;
public String getUsername() {
return uname;
}
public PageReference sayHello() {
uname = UserInfo.getName();
return null;
}
public void setState(String n) {
state = n;
}
public String getState() {
return state;
}
public PageReference methodOne() {
return null;
}
private String state = 'no';
}

<!-- Page: -->
<apex:page controller="exampleCon">
<apex:form>
<!-- Define the JavaScript function sayHello-->
<apex:actionFunction name="sayHello" action="{!sayHello}" rerender="out"
status="myStatus"/>
</apex:form>
<apex:outputPanel id="out">
<apex:outputText value="Hello "/>
<apex:actionStatus startText="requesting..." id="myStatus">
<apex:facet name="stop">{!username}</apex:facet>
</apex:actionStatus>
</apex:outputPanel>
<!-- Call the sayHello JavaScript function using a script element-->
<script>window.setTimeout(sayHello,2000)</script>
<p><apex:outputText value="Clicked? {!state}" id="showstate" /></p>
<!-- Add the onclick event listener to a panel. When clicked, the panel triggers
the methodOneInJavascript actionFunction with a param -->
<apex:outputPanel onclick="methodOneInJavascript('Yes!')" styleClass="btn">
Click Me
</apex:outputPanel>
<apex:form>
<apex:actionFunction action="{!methodOne}" name="methodOneInJavascript"
rerender="showstate">
<apex:param name="firstParam" assignTo="{!state}" value="" />
</apex:actionFunction>
</apex:form>
209
</apex:page>

 See this assignTo="{!state}" , that ius what you also need to do.

assignTo    :  A setter method that assigns the value of this param to a 10.0 global variable in the associated Visualforce controller. If this assignTo Object attribute is used, getter and setter methods, or a property with get and set values, must be defined.