You can style the elements yourself so that they look and feel like normal components. Alternatively, you can assign an ID to the element and use that ID to pick up the element and modify it. Use $Component to reference the element. Required attributes will still be required to render the element, so you may need a "dummy" function to populate the table or list with an initially blank value.

For example:

<!-- snip -->

<script type="text/javascript">
//<![CDATA[

// On the appropriate event, call:
// sforce.connection.*some-function*
//         (*parameter1*, { onSuccess: updateTable, onFailure: alert } )

// This function receives the results of *some-function*,
// and renders the table.
function updateTable(data) {
    var myDataTable = document.getElementById('{!$Component.myDataTable}')
    // DO something with myDataTable
}
//]]>
</script>

<!-- snip -->

<apex:dataTable id="myDataTable" value="{!blankList}" var="item">
<apex:column headerValue="Field 1"/>
<apex:column headerValue="Field 2"/>
</apex:dataTable>

<!-- snip -->

The real question may be... why would you go through this much trouble? It would seem to me that you could just push the data in to the dataTable directly and save the hassle of this design. You can even use server event-generating tags (such as commandButton and actionFunction) to re-render (using the reRender attribute) to perform the same function with nearly the same efficiency. Alternatively, you could use @RemoteAction to acheive the same results with less code.