Too bad that the game implies otherwise, anyway.
Also, simply is she can traverse dimensions doesn't mean that she has to be omni potent. If you take into account what Masato said and how Schala wrote her ending journal line, it's quite plausible that indeed, Schala did travel to our world to look for Serge. Heck, it'd have a greater effect if that was true. Remember, Schala has no place in the CT universe anymore. Her past is erased, she does not belong in the future.