Probably not. Sorry.
Snowshoe is located in the "Quiet Zone" that surrounds the National Radio Astronomy Observatory in Green Bank. At least partially because of this, there is almost no coverage while on the mountain.
Check out the following links to find out more about the quiet zone: http://www.gb.nrao.edu/nrqz/ http://www.pbs.org/kcet/wiredscience/video/308-the_quiet_zone.html
AT&T is the best bet for getting a signal --- but even though it's the best, it's still marginal and probably wont' work most of the time.
Verizon/US Cellular/Sprint -- typically have no coverage at all -- in fact I lose coverage about an hour from the mountain
To make things even more complicated long distance calls are blocked from the land line phone in the unit.
If you bring your laptop, you can always login to the free wi-fi connection and use Skype or google voice to make calls out.
If you are leaving your technology at home you should be prepared with a calling card (you can get one from Wildcat Provisions too)