Yes. When you initially go descend into the cave, you go down several flights of stairs. And at the end, you have to go up…but not as many, IIRC, because as the tour progresses you slowly work your way upwards.
Check out this site for a more thorough description of the cave tour: Attraction of the week: Silver Dollar City's Marvel Cave
I can’t speak to that directly…but I can say that the park itself is on the side of a mountain, so there is a lot more physicality to the park than the likes of WDW. Just take your time.