"Workplace" accounts are completely separate, with the exception of an optional link to your personal account to make it easier to log in. To my knowledge, no other data is shared. Your employer owns the data, not Facebook.
Maybe not now. But they have it. And correlating it would be trivial.
I'm already annoyed that I get my two factor codes from two different apps (one for Facebook, one for everything else), I'd be extra annoyed if it had to be three.