Actualy, I would say having two specialities is pretty common in Star Trek. Geordi was a pilot-Engineer too. Worf a secutity-operations guy (what he did in season 1 and when data was suspected to have died), O'Brien was tactical and engineer. Tom Paris Pilot -Nurse. Well actualy that was because of a lack of other nursing staff, but if you take in mind his interests he probably was looking towards engineering/science besides piloting (which was why he had taken biochemistry in the academy).He wasn't even a cadet and he was the main pilot and an engineering wunderkid.
A cadet or junior officer can probably cover multiple stations but they won't be the red alert operator of those stations.
Not saying Wesley wasnt written horribly, but I think with good writing you can get away with it. And as I said, in the third and fourth season Wesley was written better and less annoying, even though he was a pilot-engineer.