Fetch views using a ajax request
Yes it is very much possible, but probably you can do it only by creating custom module.


send Ajax request to the Drupal
load selected view form database by views_get_view
execute selected display by $view->execute_display('display')
send HTML created on executing display back to the client.
on client side put this html wherever you want


Check ajax load module (which is D6 only) too, maybe it can help you.

There is a even quicker way and more robust to render a view: views_embed_view