That wasn't what I quite meant. In his mind at the time, the Gods were either malicious, uncaring, or useless. Which makes them unworthy of worship. And unfortunately, the Storm God is really weak right now and can't do much. So, why worship him?
Judging by his story about the hawk, sentimentality won't go very far. Why the Storm God and not some other more immediately powerful and useful God, if he wants to sacrifice or pay homage to one?
I kind of feel like that it's definitely going to be something that's brought up. The Storm God has a personal connection to the Baratheons which definitely helps, but this is something that Stannis is going to really need to be sold on.
Even when R'hllor proved his power and usefulness through Melisandre multiple times, Stannis was kind of a reluctant believer.