Yes, you can #include asp files into aspx pages, but I think you could run into trouble if you have asp server side code in those files. One, there is an "ASP Compatibility" page directive you can use in your ASPX pages that might help. Two, ASP and ASP.net use different Session mechanisms, so a session var in ASP may not be available in ASP.NET.
For Headers and Footers, I find creating ASP.NET "user controls" to be a better solution than includes. Once you master user controls, you will never need to use include files again.