Yes carriers have more reactors than subs. Not every member of either crew works with the reactors. In fact, a small fraction of a carrier crew does and typically less than half of the sub crew. Even then, most of those are enlisted. Also, officers have a set qualification path which differs from the enlisted side, that I will let one of the people that have actually walked the path speak to, so you need not worry about your opportunities to "work with the reactor."
Justin