In terms of the fluff, it makes sense that the fighters get the +1. The rule says the admiral 'has trained his fighter crews accordingly.'
In terms of rules, the player is getting the benefit of an Admiral's ability without fielding the Admiral in his fleet selection.
Personally, I would be tempted to say yes. Largely because I don't think it will make a huge difference. It is open for abuse if the Admiral is on a Poseidon and the player wishes to field 6 wings of thunderbolts, but generally a +1 bonus on a few flights isn't a game breaker.