The trouble with getting anything up to escape velocity or higher low down is the energy lost to atmospheric friction. It makes no difference if you're using a linear accelerator, a chemical cannon or a big crossbow; you're going to vaporise half your vehicle, and all that energy is lost as velocity.
Even if you run your barrel/track up to the top of a mountain there's too much air above you, and diminishing returns since friction increases much faster than speed.
Perhaps as the first stage, pushing a rocket or Laserlifter up to a good starting velocity, so their inboard propulsion system could take over from there?
Of course, if you could mount the cannon in a very big zeppelin, and use a proportion of the lifting gasses as fuel…