You can't drop your existing application into DNN and utilize DNN functionality. No, you can't.

DNN consists of modules, and you have to change your application in DNN module paradigm. By using IFRAME, you can easily show to client about your app, but you will lack DNN functionality. So, my suggest are:

1. Try to do refactoring your application into DNN module (if you have no time to do that, try to outsource to third party company). Because DNN only one 'door'. That's default.aspx, and modules is only collection of web user controls, so you have to convert your .aspx into .ascx.
2. You will need to do some data migration from exiting app into DNN app (especially about your user member) because i believe that your user member management will be different than what DNN does.
3. Testing, testing and testing. :) Yes, I know that this step need a time to do.

That's my opinion.

HTH.