Actually, no, I don’t think it does.
I see the Royces as something of the Vale’s Loyal Opposition. They’re one of the most powerful Houses in the Vale other than the Arryns, they’re older than the Arryns (and Valemen are super-snobby so this counts), and no one challenges the Arryns except for them. Hence why a Royce cadet branch ended up at the Gates of the Moon, why we see Royces as Lords Regent of the Vale, why Royces marry into House Arryn (and I would imagine vice versa), why it was the Royce of Runestone who besieged Jonos Arryn when he turned traitor, and why Bronze Yohn was one of the first to turn against Littlefinger.
I see them as somewhat assimilating and somewhat accomodating. On the one hand, the Royces have converted to the Seven and are definitely bang on side with the whole idea of knighthood and tourneys and the like. So they’ve done the big ticket things that matter. On the other hand, they’re very proud of their First Men heritage – the runic bronze armor, the marriages into House Stark, etc. – but I think in a way that works for the Vale. Being arch-traditionalists, the Vale are very into heritage, and the Royces being Seven-worshipping knights means that the First Men stuff is made “safe.”