I'll answer my own question. I hope it helps other developers/users. The answer is yes. It is possible to use Tiles with Ajax4Jsf.
I wrote a PhaseListener that checks to see if this is an ajax request. I have a specific scenario that I'm addressing, so I'm using a request scoped attribute that tells me when it is Ajax. Then during the render_response phase, in the beforePhase method, I call the AjaxContext to render the page.
FacesContext context = pe.getFacesContext();
AjaxContext ajaxcontext = AjaxContext.getCurrentInstance(context);
//Render the response
that does it -- renders the page, bypassing the tiles view handler. One other note: if your site is XHTML Transitional, reset the content_type in the afterPhase of render_response to text/html. Otherwise, the AjaxFilter always sets the content type to text/xml, regardless of the forceparser parameter setting. This will break any pages that do not adhere to xhtml strict.