You should be fine to compound it. Just be smart and don't build up heat. Moving quicker and not letting the pad heat up in one spot will prevent a burn, it's just plastic after all. Try a medium cut polish first and see if that gives you good results.
You can polish with something finer than a compound (I used Sonax Perfect Finish) but know that unless you pull off your emblem you will have a noticeable haze line around it where you weren't able to reach.