Wow.. This is a must for me to reply. I was in your shoes about 23 years ago. Dare I say exactly--with a twist.
Graduated BSME from University of Florida. I wanted to be a pilot, and actually had to "trade in" my ROTC engineering scholarship to accept the pilot slot. Unfortunately, after graduation, they cut pilot production nearly in half, and I was randomly in the "cut" half. So they sent me off to be an engineer anyway! I did development engineering (62xx was the career field if I remember right). It was good engineering experience and I designed parts that I would eventually fly later as a pilot. In the process there, I got my Masters Degree and the beginning four-years of engineering experience was enough to eventually get my P.E. license. After winning a major command engineering award, I had a chance to tell the ranking guy my story, and how I wanted to fly. Three weeks later I was in flight school, one year later I was flying an F-16, and a year after that I was in combat over Iraq.
With this background, I will offer you the following:
1. Most of 62Es comments above are spot on. There is a lot of mis-info otherwise, so proceed with caution. I.e. the flying commitment is EIGHT YEARS after a year-long flight school.
2. You fly, because you want to fly. Expect to fly a lot. That is if you get through flight school, and all the other rigors--it's not a given. You typically won't have time to get a master's while you are operational. They demand your full attention and then some. If you try to juggle flying/family/masters, expect failure in (at least) one of the three areas. Operational flying is--among other things--a leadership factory. Young men go in, leaders come out three years later. Then they expect you to lead.. or you could go to test pilot school.
3. Lately, if you are at the top of your class, you may still get an unmanned aerial system (UAS). I.e. flying a predator in Afghanistan from the desert in Nevada. This may be a fit for you. In fact, if you let it be known you WANTED this, you'd probably get it. This seems to fit an engineering mind better than other flying jobs.
4. In the F-16 squadron I kept my engineering skills on the down-low. People looked at you funny if you rattled off too much in-detail info. You really have to temper some of the skills you developed to fit the culture, but you learn new skills. "Paralysis by analysis" will no longer exist for you. You will be an expert in risk management. Your quick-math skills will save your life one day, or lack thereof will kill you. I stayed fresh on my own though by getting a second master's degree right before retirement (in a non-flying job), and just lots of tinkering.
5. Evaluate design applications and requirements. You bet. In fact, as a pilot, I got to fly with a piece of equipment I designed as a young engineer. I'm happy to say 20 years, later, the structural fix I put in has had zero failures. As the "user" you have a mysterious sense of credibility when working issues back home.
6. Now the dark side. The flying game will end. As an analogy, it's like a professional sports team... They keep 'em young, and when you get older, you go on to do things like coach, or commentator. When I was one year out from retirement, I prepared a flying resume for the airlines, and an engineering resume as well. Airlines aren't hiring--I expected that. But ah ha! I've got engineering as a back up! I must have sent out 1000 resume's over the course of a year. It wasn't a bad resume: MSAE, BSME, P.E., but the experience--although four years of really good work--was 15 years old. I received exactly one engineering interview, and that was only due to my F-16 experience. When we came to the salary discussion, it was so shockingly low, that I simply could not accept it. I'm afraid if I am going to get back into engineering, I'll have to start my own company or something, because the phone's not ringing off the hook. The good news is that I found an aviation consulting job that quite literally doubled my previous salary, and I only work 6 mo/yr. At this point, I'm happy "tinkering" in my six months off, contributing my engineering to the open-source gang. I still miss "real" engineering, and I send out resumes looking for that perfect fit between aviation and engineering, but I'm not holding my breath. Aviation folks don't care much about masters degrees and P.E.s, Engineering folks don't care much about type ratings, flight hours, or emergency procedures.
Would I do it different? No. But I wanted to be a pilot first, engineer (close) second. It looks like you may have these priorities transposed, which will change your game plan.
BLOB: (bottom line on bottom) If you want to be an engineer, turn down the pilot slot. Be firm with your recruiter. As an engineer they will send you (full pay) to get your ENGINEERING masters among other things. You may design a little, but once you make Captain (if not before) you will be in Engineering Management, managing $million if not $billion contracts. You will see everything. You will develop engineering skills, leadership, and precious contacts in this regard.
If you want to be a pilot--but your heart still tugs to do engineering, then go to pilot training, do well--(and you will do well as long as you don't over-think things) you can get a UAS, or take a jet and try to go to Test Pilot School (TPS). If you get TPS (competitive position after 1000 hours of flight time), they will send you to get an Engineering Master's Degree, then on to Edwards where you will fly every airplane in the inventory, and have a real shot at being an astronaut.
Regardless, the world is yours. Make a decision and go get it.
-Darrell
ret USAF