It would only negate 6% of the cost of going to orbit. And you'd have to pay that 94% pretty quickly to not fall down.
Except that it would be better than that, because rocket nozzles work best at a specific external pressure, and getting to launch your rocket in vacuum means you can design your engines for strictly that.
There are occasionally some ideas of launching rockets from tops of tall mountains, like Kilimanjaro. The advantage directly gained from being 6km closer to space is negligible, but the advantage gained from being able to use more expanded nozzles would be substantial -- albeit likely not worth having to haul your rocket up a mountain to launch it.
You would fall back down to earth. The gravity of the earth at the "space" barrier is slightly less than at the surface, but not all that much. So without the speed to maintain an orbit, it would be like falling from an extremely tall ladder.
You would just fall back to earth, gaining a lot of speed and then getting destroyed by the atmosphere. Even the force of gravity where the ISS is is pretty similar to at sea level.
What would happen if we were able to make it all the way up to space, vertically, but not gain any horizontal speed?