Just my opinion....I would think not*. At the end of the day, its what you demonstrate(having a good demonstration/example of your work will carry more weight than a piece of paper). Having hired a Full Sail graduate and a complete audio newbie(around the same time), the newbie was mixing "name artist" shows within a year, while the FS grad was relegated to working a small lounge.
*Having said that, if you DON'T have any musical skill/knowledge, there are certain things a music engineer really should know(such as basic harmony theory, chord structure, song structure, the basics of Nashville Numbers....basic knowledge makes it much easier to communicate with musicians). I you are moderately proficient on some instrument, you likely have that covered
