Well, you're not likely to be able to get 24p video to work right in Premiere Elements regardless.
That said, no, the difference in frame rate alone will not cause your audio to go out of sync.
What you'll more likely see is poor blend of frames in your video. It might look jaggy or fuzzy on output.
That is IF it works at all. Premiere Elements technically only supports 25 fps PAL and 29.97 fps NTSC.