First of all, I think you're in for a better lifestyle, overall, for choosing engineering as a career, instead of flying.
In general, I agree with what has been said. I would say that it most likely isn't worth getting your A&P solely to put on your resume. That said, though, it *will* obviously make your resume stand out, all other things being equal. If you have some interest in that side of things, getting your A&P will make you a better engineer (re: what was said about designing something that just doesn't work), and you will benefit from having some background information for some of your engineering classes that your classmates won't have (even though the A&P training doesn't have much in the way of theory, compared to engineering).
In my case, having an A&P also helped me to get an engineering internship before I would have been competitive based on my university classwork alone. More internships helped during the interview process at graduation time.
If you're interested in getting your A&P, I, too, would recommend trying to do it at a community college starting as soon as possible--even during high school if you're able. As someone noted, it will take probably take 18-24 months to finish your A&P, so your college classwork might have to flex around that for a semester or so--not a bad thing.
Best wishes on your decision! PM me if I can be of further help.
Edit: Regarding your question about part time study while attending college? Maybe. A&P classes are not flexible, (FAA requirements regarding attendance, etc.) but there are some that are structured part time/evening. My classes were Mon-Thur evenings 5:30-10:30, which worked out great with my job, so it could be done.