I've not yet met a swirl that I couldn't get rid of with the PC - although it will take a lot longer to do so.
You'll probably need to go to a more aggressive polish using the PC compared to a rotary, but I wouldn't shy away from the PC only for that reason.
Having said that, I did find that things got much better for me when I got away from the Griot's Garage (specifically formulated for PC???) polishes and tried Menzerna. The difference was like night & day.
Take it slow until you get used to it, and until you know how abrasive of a polish you need, and I'm sure you'll get the results that you want.