I've been a partner for a few years now, and mind you, I do a lot of covers.
If it hasn't changed from when I joined, basically not much changes.
You may get a few enhanced options on your account, such as being able to add more graphics to your channel and have the auto-play function on your vids (not sure whether these features are still exclusive to partners, or regular members can do them too.)
When you upload a new video, you have the option of putting advertisements on that video. ie: if you choose to submit that video to earn revenue, it must be all-original, etc.
If you select not to have it submitted for revenue, then your video would just be uploaded normally as before without the copyright shenanigans.
I only turn on revenue for my original work, and just upload covers without the revenue on. Haven't run into problems yet.