I've seen people riding them all the time up and down the GAP.
I've done the GAP from Pittsburgh down to Connellsville, using my hybrid with cheap nashbar 700x32c tires and it was fine. From Pittsburgh to little Boston it is paved after that you get into the crushed limestone. After a heavy rain you can run in to some muddy parts.
I've done Pittsburgh to DC and the Great Allegheny Passage is fine for a cyclocross, particularly if it's dry. I've even seen road bikes on that section. If you're going beyond Cumberland, MD, however, the path gets rougher and muddier. Have fun--it's a beautiful ride.