Can I roll drywall mud over paneling? Will it hold up over time?

I think you would be better off to take down the paneling and putting up new drywall. Although this will take more time and is more work 1- it will look completed and 2nd, you're talking about a basement, which is mostly below grade. I don't know if you put the paneling up to begin with, but in my experience, paneling is usually a great way to hide things. At least this way, you can see what is going on behind the paneling and address anything that needs to be fixed.