Nnnoooot exactly, but close enough.
It's more like an Invisibility or a Sanctuary spell, where you can't be seen, or can't be attacked, in exchange for not being able to attack or cast targeted spells yourself.
Pilar promises not to remember herself, or make any attacks or targeted spells, or steal anything or... do anything imbalanced, one might say, though that part has to do with ancient godagreements and not just the structure of magic. In exchange, other people don't remember Pilar either, and she doesn't set off alarm spells.