There are two answers to this:
Answer one
Strictly: No. Personas aren't like Stands. They don't have powers specific to the users personality (ironically). Personas kinda all have the same "powers", those being: great strength, durability, speed, element manipulation, matter manipulation, psychic powers. Basically the various skills in the game. The closest thing to what your character does would work very well as a feature of a Navigator type persona, like Himiko and Necronomicon. A persona not designed for battle but for psychicly navigating the metaverse.
And answer two
Narratively: Yeah sure, why the heck not. Have you read Detective Naoto? Have you seen the ova Persona Trinity Soul? Personas do all sorts of shit in those mediums. Personas pretty much act like Stands in these things! They may not be cannon but it's still persona related. At the end of the day, Personas not the type of series to really spell out all the rules and leave no room for ambiguity, so that's why writers typically have a field day when they're given the material.
Ultimately just have fun with whatever character you're making. If you wanna keep them closer to the cannon of the games and more "accurate" maybe make her persona a Navigator type or maybe if she's a resident of the metaverse like Teddie she can have a unique power.
If you don't care so much about cannon and just wanna write something fun then as Arsene put it "Run wild to your hearts content" Personas technically don't have rules, so go nuts.
Hope this helps, and good luck on that character