I’m almost done with my bachelors in ERAU, after attending 3 schools (2 of which were not aviation related) I think that the aviation degree comes to improve your aviation general knowledge, but is not critical for a flying job----is good if you want to follow up with a master in aviation safety or something like that.
Having said that, if I were you I would go for the practical phase of your career (go make some hours) and do your MBA as you mention.