Ah ha! Found it. To wait until an AJAX call is complete when the site uses ExtJS check the following javascript function:
return Ext.Ajax.isLoading();
It will be false when all AJAX calls have finished. So, then my code becomes:
JavascriptExecutor executer = (JavascriptExecutor) driver;
Boolean ajaxRunning = ((Boolean) executer.executeScript("return Ext.Ajax.isLoading();"));