Short answer:
Yes, it could be made to work. As has been pointed out, a launcher at least 20 km long would be required, especially considering drag, and the business end of it would have to be well up the side of a very high mountain.
The kicker is that I don't see even the most optimistic financial forecasts of the suborbital tourist business justifying the massive capital expense of such a thing. While you were halfway through with construction, other outfits using carrier aircraft or rockets would have long ago eaten your lunch.
There's more to this business than technology and physics.