>Is there a way in ASP.NET to obtain a page response but to also initiate a download once the page has completed?
Yes there is. It takes a little javascript and an AJAX-style partial postback to get the content. I haven't coded it myself, but you can see it working at msn. You could also use a web service and the DHTML Webservice Behavior to return the content after the response:
http://msdn.microsoft.com/library/default.asp?url=/workshop/author/webservice/overview.asp.
Put an empty DIV on the page then stuff it with the content by hooking the onLoad event in BODY.