No, you cannot. Sorry, fam!
Sound-a-likes--or cover versions, or tribute songs that sound verrry similar to the original--aren’t accepted by libraries.
The original artist, label, and/or publisher has grounds for a lawsuit if it ends up being sync'd. So it's a hugeeeee no-no in the library world. This lawsuit, would ultimately - end up on your doorstep, not the library or That Pitch's.
Even on the rare chance the content doesn't violate laws, it may confuse customers. Which is why libraries and their legal teams give it a flat-out no.