Types of check eligibility for monetizing
1) Video - you will need to show some proof that you are owner on 99,9% of all videos you will upload (not only music videos, even real life cam videos,etc..) -Even if there is no reason to expect copyrighted content.
2) Audio - first there is auto check if music is copyrighted - songs will be declined only if it will be exactly the same as original(speeded song version will behave as cover) (you can monetize cover and you will recieve like 66,6% of income from ads), then some slow check in next few days.
By the way: there is always option that somebody will report you and videos get banned instantly. -THIS IS THE ONLY WAY YOUTUBE WILL BAN YOUR ACCOUNT - 3 VERIFIED REPORTS (3 WARNINGS AND THEN YOU GET BAN).
ou can upload 100 copyrighted songs, there can be 90% music of declined from adsense to monetize, but you will not get any ban or anything. You will get ban only if people/artist will report your videos. You can always reupload deleted songs again and again...
Summary: you will most probably not be banned. They will only delete your songs after few days if you will upload speeded up/modified versions. Also they wont delete songs that are free(mixtape) or 90% of cover versions. If you will upload some famous song without modifying it you will not be able to monetize from moment you will upload....