Shutout...
I know you are looking at the Navy, but I felt a couple cents worth wouldn't hurt. I went through an aviation-program college before I went through Air Force pilot training and I did OK. Not great, but good enough. What I wanted to tell you is that it all depends on you. It depends on how well you can forget some of whatever you've learned before and learn what they want you to learn. FAST. That's the key. We had four guys in my class get fighters - one had never flown a plane before (except for Flight Screening immediately before UPT) and the others had only minimal time, i.e none had come from aviation-related schools. We had one guy who was a CFI and had flown Part 135 turboprops all during college and he struggled in UPT at times. I later ran into one of the guys (who had smoked through UPT, BTW) who had gotten an F-15. It was about 4 years after UPT. I was at United for some sim work when I saw him, and he was about to bust out of 727 training because he couldn't pass his sim ride. The systems were giving him fits! Bottom line is, prior flight experience is really no predictor of performance at UPT.
I would agree with Skywiz to diversify your education. If something happens in your career you'll need something else to make a living. An aviation degree won't really help you in pilot training no matter which service you're in, but IF, heaven forbid, you ever need to do something else, an aviation degree will be nearly worthless. I did it because I just couldn't wait four more years to learn to fly. It doesn't mean it was smart though.
For you right now, it boils down to doing what you think you need to do to reach your goal. No one here but you can know what that is. We can just give you our experiences. I actually left the engineering program at CU Boulder because by year 2 I knew my grades would not be good enough to get a pilot slot out of the ROTC program I was in there. That's when I got into an aviation program and joined the Air Guard. Not only did it help me pay for school, but while enlisted there I made the contacts necessary to get a pilot slot when I graduated. That route worked for me, your mileage may vary.
Definitely do SOME flying before you go though. Maybe even do some instrument work, flying absolutely as fast as possible. You'll learn to talk on the radio, and get the general instrument concepts down, but that's about all you'll need to know beforehand, and that's about all the knowledge that will transfer in any case.
Best wishes!