Can clear nail polish get rid of a boil/abscess?

No, for several reasons. First, unless all of the bacteria are removed from the abscess (not possible), then the nail polish could act as a new cover and recreate the abscess. Second, not all bacteria require air to live (Aerobic bacteria) and in fact many nasty ones survive much better without air (anaerobic bacteria). The keys to healing an abscess are to have it drained and then get the cavity to heal. You take antibiotics not to heal the abscess but to help the surrounding tissues fight off the bacterial infection. Put a thin layer of triple antibiotic on the abscess opening every day and keep it covered with an absorbent dressing and it should heal just fine.