This question keeps coming up.
Reverse the roles: Imagine I’m an Industrial Designer and want to get into Graphic Design. Do you think I could self study and apply for a masters program?
What are some of the challenges you think I will face? Do you think I can compete with people who have a BA in Graphic Design?
The answer is always, yes it’s doable but you will face challenges. It will also depend on your skill as a designer. A title/degree is worthless if your portfolio is not up to par with the rest.
Do you have any other more specific questions?