My experience: most of my apps work fine without Google services. Even more advanced apps - sometimes they just can’t verify licensing, so may complain occasionally. Even now, Macrodroid can’t verify licensing through microG, but the dev has a process for licensing with a serial key based on your Google account.
Nah, they already have your email, and Play services could track that too. They just want to make sure they’re the only ones tracking your email.