I didn't carry my cell phone on my last trip but one in our group did make a phone call at Ivestor gap and sent texts at a few other points along the way. I believe he had Verizon.
Good luck you will definitely enjoy yourself. The trail is well marked and easy to follow just about everywhere and should be easy enough to solo. The most confusing point is at Shining Rock. There are about 6 trails and none are marked. I have done it twice and both times ended up on the wrong trail but it still leads to the same place, ivestor gap.
I might also recommend 2 maps. The Shining Rock Middle Prong map is much more detailed but only has half the trail on it and the larger Map that has the entire trail is obviously a must.
The best water source of the trip is off the black balsam spur trail that goes to the parking area. Its a steep hike but there are some drop toilets there and if you make a right on the road about 200 yards down there is a pipe with spring water that doesn't need to be filtered.