Of course it will affect your shot at getting in, just as it will at pretty much any private college. For the most part though, I think that whether or not you are applying for FA will only effect you if you are on the cusp between being admitted or not. If you're a strong applicant, you should still get it, or so I hope!
Sending the letter sounds a bit unnecessary though - plus what happens if you decide to attend Bates w/ a small FA package and then end up not getting much FA from other sources? It's best not to accumulate debt in UG unless absolutely necessary if you're planning on attending graduate school, so just keep that in mind.
Good luck