Correct. Thor has innate powers unrelated to the hammer. The hammer makes him much more formidable, but his status as "god of thunder" which allows him to summon storms and control weather, generate raw "godforce" from his body, and his massive strength all predate his being able to pick up mjolnir. His mother is also an elder god, more powerful than Odin and Thor has some Ill defined earth based powers related to that.
There's also the issue that Jarnbjorn while not mjolnir is still DISGUSTINGLY powerful, and Thor just killed exitar (!!!) With it in uncanny Avengers. Mjolnir as impressive as it is can't get away with that one.
So Thor is still technically the "god of thunder" without the Mjolnir? If this new character no longer has the Mjolnir, will she loose her thunder powers?