Q: Can I get rid of Classic for good?
A: Yes
Q: How do I do it?
A: Drag classic to the trash
Q: Is OS X affected at all?
A: No, classic should not be affected.
I know that you may not use classic but it's always a good idea to keep it around. You never know when you may need to fire it up.
If you are running out of disk space or classic is causing issues with your computer then it might be worth it, but as I view it, it's my spare tire for whatever may come down the road.
It's our DOS to Windows 95... you sure hope you don't need it, but it's nice when you are in a pinch...