I don't quite follow what you intend to do, but I'm very confident that, yes, there is a way to use HTML::Template and CGI::Screen together to present multiple screens on a single page. It doesn't strike me as an entirely reasonable thing to want to do1
, but there's probably a way to do it anyhow.
Perhaps if you were to explain more clearly just what you want to accomplish - as in the desired end result, not just a list of modules you (think you) want to use - then we might be able to advise you more effectively.
1 Judging by the CGI::Screen docs, I expect that it would be easier to do... whatever you're trying to do... with HTML::Template alone than to shoehorn CGI::Screen into producing components that can be placed into a page, when CGI::Screen really wants to be creating and sending complete pages.