Answer
Yes — for the current session's User ID (identity), use &APPOWNER.FND_Session_API.Get_Fnd_User; for the corresponding Person ID, use &APPOWNER.PERSON_INFO_API.Get_Id_For_User(&APPOWNER.FND_Session_API.Get_Fnd_User). Both can be used directly inside a Saved/Advanced Query's condition (in place of a hardcoded literal value), so the same shared query dynamically scopes its results to whichever user actually runs it, rather than needing a separate copy of the query per user.