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".
It serves a purpose. But, in practice it means 1/3 of my life is spent doing nothing but checking the clock to see "Am I not dysfunctional yet? Nope. Dammit."
That is an individual effort. Reducing one's sleep can be done. There are processes to do it. You have to make your subconscious more efficient at processing. During sleep your mind makes subconscious connections and processes events of the day. By practicing different forms of meditation it can allow your mind to do that.