Does my application to the Honors College impact my normal application to DUS?

Colleges and Universities A-Z Penn State
1

Was just wondering

2

no, it doesn’t. Those are totally separate processes.
Of course, you can’t get into Schreyer if you don’t get into Penn State :D, but as DUS even if you don’t get into Schreyer you can sign up as a Paterno Scholar Aspirant (something like that).