Of course, since they are virtually guaranteed that promotion, it would be a very brave or very foolish officer who gave them more than a token admonishment...
Yes and no...that "guaranteed" promotion might not come off if the guy's family lacks enough influence - plenty of noble families out there competing for limited chances at this sort of thing. Just like in the bad old days of the RN families had to petition to have their youngsters be taken on board - and depending on the reputation of the captain the competition might be steep.
Yeah, you might torpedo your career if you failed some spoiled brat from an influential family, but historically the RN and how it handled nobility in the ranks was far different from the Army's way- no purchasing of commissions, His Majesty's ships were not trusted to someone just because they had a title but were otherwise a blockhead of a seaman, everyone had to pull their weight and present their papers to be judged fairly by the Promotions Board.
After all, unlike the Army the enemy tended to snipe officers on the decks (surprisingly small decks, too) of ships and in close quarter fighting even a 12 year old middie might have to go hand to hand against boarders or direct a gun division that's blasting away at another ship only a few yards away. So ineptitude wasn't tolerated for the sake of titles - a captain would just find a way (at worst) to foist the young fool onto someone else.
Now yes, to leap that vast chasm from Commander to Post-Captain it helped to have influence, but nobility was not
required to do it...it mainly helped with assignments to staff and to get you closer to some plum job that would help you enter the peerage and influence policy. For the most part promotions were otherwise based on merit, but there will always be that behind the scenes politicking going on and that's mainly what I was referring to as ripe for role-playing.
In any case a lot depends on how much weight you want nobility to have in your game. Me, I run it just like I said and as a result the Navy may be the preferred glamour service for the nobility but you can't buy your way into it. If you want that sort of thing you can do it with the Marines or one of the colonial forces, but His Majesty isn't going to trust some noble fop with too much money and not enough sense to command a ship. Better to just let him pull a term or two as a lower officer so the family can brag about junior being in the Navy and then send him gently on his way to the rest of his "noble career" before he gets anyone seriously hurt.
It still happens once in a while, though, but that adds to background color and interesting characters for the players to run into, like the Count I have currently flying around in this trade war with his own 300 ton privateer. The guy has honorary titles, commands a Colonial Guard unit of hussars, but since he's getting on in years and has yet to see real action he wants to get into some so he can uphold the family tradition before he's too old.
He's got a little Four Feathers meets Lord Cardigan thing going on but he's lots of fun for the players to run into. They taunt him mercilessly since they've defeated him twice already, but it only makes him more determined. I mean it's gotten so bad that some of the local casinos on the world they most often are likely to run into each other near or on have started setting odds on the winner of the next round.