No, this does not change anything. If it is written in such a way as to be legally binding, it's legally binding. If it's not written in such a way as to be legally binding, then it's not legally binding. We are now in contract law, not employment law.
Of course, if it's not written in such as way as to be legally binding, THEN the fact that FL is at-will may be a factor. But it does not affect whether or not a contract is or is not legally binding.