Many places are trying to get in on the ESkyWarn set up. We have a kind of skywarn net on the Midwest GMRS net. Its not official and not monitored yet by the NWS, but there are quite a few of us Spotters that keep everyone informed on the net. (WRVU445 is my call.)
Check the ICS 205 for your Skywarn area. Ours lists GMRS Chase channels. Nothing specifically for nets, but that would fall under your Net Manager's assignment. If you are a NCO, and think there should be a need for a GMRS net, stand one up and let the Area and Net Manager know that you did it.