Fedora, not AFAIK. But there are other embedded/mobile oriented Linux projects. Take a look at:
http://handhelds.org/moin/moin.cgi/SupportedHandheldSummaryI believe your iMate JAM is a rebranded HTC Magician.
Note lots of "NO" in the "Ready for users" column.
However, we can always hope that the advent of Google's Android platform may turn this situation around...