It's 100% dependent on how deep the scratches are. You say they don't appear to be "through the paint". Are they through the clearcoat? Or just in the clearcoat? Are they deep enough that you can you catch your fingernail in them?
If they're in the clearcoat and not deep, then normal polishing *may* minimize them enough to make them nearly invisible - doesn't eliminate the scratches, but polishes the edges of the scratches to make them "blend". Doing spot-polishing just on the scratch using ScratchX or a similar product and a hand applicator may be a lot faster than using the PC for this type of work.
If they're a little deeper, it may require more aggressive polishing (e.g. with a rotary) to minimize them.
If they're even deeper (but still in the clearcoat only) then wetsanding may be in order. CAREFUL. I've done this with good results on my MINI. I've also wetsanded all they way to the color coat on our minivan (ouch). Not something I recommend unless you have something you don't care about to practice on and learn on.
If they're even deeper, you may need to add some clearcoat (or base coat, if they're through the paint) and then knock it back down with wetsanding or rotary.
But OctaneGuy is the expert. I just regurgitate what he's taught me, mostly.
But I'd start with ScratchX by hand - then work up in aggressiveness. Polish and rewax as ken suggests after the scratches are taken care of...
