Well, I suppose that would depend on the rules of the magic system and the purpose of the ritual. But in this case, I'd guess it's pretty likely that yes, you can?
In terms of the kinds of rituals P does, I think so? For one thing, Storm doesn't get told much about what's going on the first few times he helps P do something, and those don't seem to be at all diminished in effectiveness for it.
For another, it's a common thing in magic that's about re-enacting narratives to harness their power that certain actions get done by the correct person, the person who's authorized to do the action. Like, only the youngest prince can break the spell on the castle, in the fairy tale. So you might have rituals designed to make someone count, temporarily and via a loophole, as the correct person. Like... you do something to age all the other princes, suddenly you're the youngest prince, just long enough to break the spell. And the prince doesn't need to know what he's doing to do that, the enchantment only cares that he is, right now, for whatever reason, in fact the youngest.
For another thing: recursion. The way P talks about recursion, it sounds very much like something that can happen to you without your noticing. Therefore, it must be possible to do it without knowing you're doing it. But recursion fits the definition of a ritual: it's a set of meaningful actions that have a supernatural effect. So if it's possible to go through the motions of recursion unaware, and it still works, then that would imply it's possible to go through the motions of a ritual unaware, and it still works.