Absolutely! As long as you maintain a consistent schedule of 3 lessons per week at a minimum, you will progress very quickly. Flying regularly is more than half the battle to retain knowledge. The part-time route may also be beneficial when learning plateaus occur. Taking a short break, doing some ground instead and simply getting your head of the cockpit for a few days can help your brain make the right connections.
Not to mention that you will be keeping your job, and your finances won't be taking as much of a hit. If for any reason life gets in the way, you will still have your job to rely on. Or maybe you'll decide that you love flight instructing and would be very happy doing it as a side gig. A good plan B is always crucial in this industry.
Good luck!