I rode the entire GAP on a hybrid, with front suspension fork, back in 2011, and rode various sections over the intervening years. The trail is crushed limestone, as others have said. It's pretty smooth. On the first ride, I used the suspension. On the rides since, I've locked it out, riding on 700x35 tires at 85 psi. Very doable. Energy-expending wise, I'd say the GAP, when dry, is probably 1.2 to 1.3 times what smooth asphalt uses. In the wet, maybe 1.5 times smooth asphalt.

While you could easily ride it on an MTB (I've ridden sections on one with 26x2.00 tires), I'd say it would be overkill. If that's the only bike option you have, I'd really consider changing out knobby tires for semi-slicks.

And to give you my fitness level - I'm 55, with creaky knees, a neck and back that aren't too flexible anymore, and arthritis in my hands and feet. I rode the full length after owning a bike for less than 6 months and with my prior max distance as 25 miles. I did 50 miles a day, but wished I had done more like 40. Two days were in rain, one day sporadic, the second in a 5 hour steady rain (challenging, but rewarding). After day one, I wished I had prepped better, but I got through it.