If your body had enough sleep that night (6 hours, uninterrupted) and you aren't sick or otherwise stressed, then yes, power through.

Getting sleepy is your brain telling you to preserve energy. Only sometimes it does that because something about the work itself bores, infuriates, disgusts, or otherwise upsets you.

That means getting "procrastination-sleepy" is your brain trying to prevent spending energy on the miniature emotional turmoil "breaking procrastination".