If your random orbital isn't some cheapo, i would think it should work. Maybe it doesn't have enough speed to do the job
. Or as a previous member had mentioned, you may need a more aggressive pad. I had fairly decent swirls on my 350z and I used a foam pad with Meguiar's Ultimate compound. The finish was flawless after I was done. I can't imagine that you have bad enough swirls that it wouldn't work.