You wouldn't have a GUI app running on a web server. You could have Windows service running and communicate with using your preferred RPC method. You could also have the web app start up a Console app in a new process. That may not be allowed by your average web host but if it's your own server then you're OK. You might also do work in the web app in secondary threads, although that may be frowned on if they run too long.
It would be my own server, a gui is being made, but more so for it to communicate with a service.
The asp would tell the service what to do, the guy would also tell it what to do.
More I think about it, the more I am leaning towards a database, with a queue, as I'd hate to have the service try and load 50 apps at the same time, but would rather it load 1,check it, continue to next....