This is what I've done as well. Fake name, profile, wildly random answers to profile questions and thumbs up to anything if I remember of have times. I only use the account to follow a couple of local businesses. Facebook is welcome to all the income that account provides them.
If you linked it to your real phone number or any of your real friends who have you in their contacts (which they've most likely shared with Facebook), you're not fooling FB.
