Each individual is capable of different levels of achievement, so of course it is possible.
That said, looking at portfolios and interviewing candidates for the past 10+ years I’d say in general MFA grads without a prior design BFA are ill prepared for the professional design world. You simply can not learn what you need to learn in 2 years. 3 is pushing it. 4 barely. 5 with a bunch of internships and you are ready to get an entry level job where you will really learn something.
This is a generalization. There are always the rare exceptions that can be cited.