Former mechanical engineer here... I'd suggest working in engineering for at least a couple of years once you graduate, and flying on the side. Hopefully you enjoy engineering, it's a pretty good field and the pay is decent. It's not mind blowing pay like some of the pilots (that aren't engineers) on here think, but it's not a bad way to live a middle class lifestyle either. By getting some post-grad work experience, you'll have a much easier time getting back into the field if you decide to try flying out and then go back to engineering.
Ultimately I left engineering after five years in the field to pursue a career as a professional pilot. By the time I made the career switch, I had all my ratings, no debt, pretty new car (again, paid off), and money saved. That was seven years ago, and I've done ok as a pilot. Could be better, but could be A LOT worse as well. I enjoy the aviation lifestyle, and won't be going back to engineering unless I absolutely have to (lose my medical, etc.).