For example, if this thing has a 10 meter circular cross-section, you'd need to be able to evacuate about 2.5 million m3 to a very good vacuum, similar to what's found in space -- in a structure that's flexing in response to a 1300 G point load. Good luck with that.
Next, when you open the door to let this thing out, there's gonna be that nice shock wave caused by air racing in to fill the vacuum. Whole lotta buffeting going on there -- launch accuracy will suck, assuming that the thing doesn't just tumble and fragment.
And don't forget the part about screaming through the atmosphere at Mach 20+. The thermal requirements are gonna be killer.
What about the EMP effects to the projectile?
I've read a plan where they planed to do this up the side of K2 getting it out of a good percent of the atmosphere (over 28K feet) before it's released. The plan was more elaborate though involving high energy ground based lasers tracking it and flashing H2O to supercritical steam thus providing thrust in addition to its initial kinetic energy. This was push mass in to Lagrangian points not just LEO.
There's not much development around K2 so no one would be bothered by the shock-wave.
Because you're not as concerned with the mass of the projectile you could surround the satellite by some sort of heavy sabot to protect it in atmospheric flight.
The problem I have with this is, do we really want all this stuff up in orbit? There's enough junk up there as it is.