All that matters is they need to see the 3 green lights on your channel settings. That's all they want to know. If you have one 1 red light you can't become partner. So if you have a copyright strike I would delete the video that got you the strike against your account.
Most of the stuff I've read says that if you have copyrighted music or whatever, to completely get rid of it before applying to becoma a partner. I'd be afraid, knowing how YouTube can be, to even have it private.
It's just safer that way, I guess. Less chance for issues down the road.