It certainly can't hurt, and demonstrates commitment toward a professional skill.
As for having time to fly on the pp license, as with any hobby or pursuit that takes travel to and from, special equipment and time, such as flying, surfing, kayaking and other activities occasionally queried on this forum, it can be done while at an SA, but it will be a challenge.
We've had a couple of our sponsor sons and daughters have their licenses before coming to USNA. Some didn't fly at all but tried to get some hops in while at home on leave. We had two who made a commitment, when they had more time as youngsters (sophomores), to pool resources and get out on Sunday afternoons to fly. They successfully obtained instrument and other advanced certifications. Of course, this was on their own dime, and they weren't varsity/club athletes or overloaded with other extra-curricular activities. It took single-minded dedication and financial dieting. One went Navy air, the other Marine air. They impressed everyone when they rented a plane to go on spring break down to NC beaches.