Yes, the guest user has a session id, but it's not valid for anything.

here is how to use ActionFucntion and databinding

first, assume you have some JS framework that wants to have a JSON reply

the JS on your app, calls  Action Function 

my call looks like this 

<!-- for loading -->
<apex:actionFunction action="{!loadData}" name="loadData"
rerender="loadPanel, updateMessage">
<apex:param name="aParam" assignTo="{!startTime}" value="" />
<apex:param name="bParam" assignTo="{!endTime}" value="" />
</apex:actionFunction>

 standard stuff, now in my controller i run a query using the start and end times

the controller then populates a string variable (with the query result) which i've called 'jsondata' 

this code is from the controller 

// pass data on new event details back in jsondata
public string jsondata { get; set; } {jsondata = '{}';}

// run a query with the startTime and endTime in mind
public void loadData() {

[blah, blah deleted... ]

jsondata = calgroup.listToJSON( cgl );
}

 normal stuff, when it's done the data is sitting in the controller and viewstate of the page.

then the trick...

my VF page has this block 

<apex:outputPanel id="loadPanel" layout="block" rendered="true">
<script>
evts = eval( '({!jsondata})' );
if ( ical != null ) {
ical.render(evts);
}
</script>
</apex:outputPanel>

So, the partial page refresh will re-draw this script panel, with data in jsondata that is fresh from the controller.

simple, clean and works.

hope this helps in your case.

PS: be sure to use something like this to avoid JS errors if you have lots of data to pass back

 -->  jsondata = String.escapeSingleQuotes( jsondata);