As far as the game is concerned: the old gods (for the most part) have bailed out. They are busy doing other stuff, and passed the responsibility of being gods onto the younger ones. Priestly powers from the old gods would be rare. The exception to that would be Tanora/Zelphia, but even then she is described to be distracted. That does not mean one cannot choose to follow one of the old gods, or be devoted to them probably. It just means there won't be the same benefits.
The relationship with the old gods and mages is somewhat questionable as well. We describe magic as coming from the old gods, but in the same sense that hamburgers come from the sun. While technically true, it is not because the sun has taken an active interest in the development of hamburgers. It is because sunlight allowed photosynthesis to occur to feed cows, and cows become hamburgers. We do not look to the sun to give us hamburgers.
The same may be said of mages. The mages take these elements that exist, simply because these gods have willed it so, and manipulate them. A fireball is not dependent upon a prayer to the gods. It is dependent upon manipulating the element of fire that Bragon has imbued in the world. No permission needed.
All this is to say: a mage can easily be disdainful of the old gods, and the younger ones. One can use a gift provided, while disdaining the giver. At the same point, a mage may decide to devote themselves to Tanora, and use only water spells, and claim that this came to be by a blessing from the goddess herself. People might disagree. At the end of the day, it doesn't matter.
Priests do not quite have that same luxury, but that isn't to say that their relationship to their god can't be 'complicated'.
To answer your question, it isn't "no, because no". It's no, because fundamentally these roles play out in different ways.
A priest will not have access to the same things a mage does. And abilities do not necessarily make statements about a person's position in the game.
A long while back, we had a number of characters playing as shamans who used magic. That does not disqualify their roleplay: a character can operate in a roleplay capacity as a priest, with 0 abilities.
The reason for 'no' in this situation is that the lore has been developed in a certain way, and the engine is going to back it.