Hmm, I guess it's possible? But then it requires quite a lot of constant fuel for your orbital retrieval vehicle. I suppose you could also "shoot" fuel up with the cannon constantly.

I'm not convinced it could be worth it. From the construction and maintenance of the cannon to the reliability of the method, even if possible, where if you don't catch a payload perfectly it just falls back to earth... rocket launches are probably more worthwhile for all this.

Since you need fuel to get into orbit you're still beholden to the rocket equation where you're using fuel that you catch to put the payload you also catch into orbit... I don't think you're necessarily that far from just using rockets, except the reliability problem.