No, you cannot. Sorry, fam!
If you are covering someone else's song, it means the library would need additional legal clearance from them for every single license. Because licenses occur at such a high volume in the library world, it can completely ruin the experience for their client and jam up their systems.
Because of these reasons (and many others) libraries overwhelmingly give covers a flat out "no." If a legal issue were to occur, you would ultimately be the one getting sued by the artist/label/publisher - not the library or That Pitch. So... help us, help you - avoid that!