Not necessarily. You just need to be clear on why it will help you in your role and be able to communicate that. For example, completing your MBA has led you to have a better understanding of the role of the Director you are supporting and that you have a unique set of skills designed to help this Director. Go into detail as to why, but be sure to stress somehow that you are serious about the EA role and your place in the company. Don't approach with an eliteist attitude about the MBA or what you can do for the company, because it's the Director who will be directly benefitting from your working there. Does that make sense? Hope so.
Please don't go down the path of not mentioning your degree. It is definitely a differentiator for you and that's a good thing!