Could. But probably won’t help how you want it. That’s some pretty severe sleep disturbance and deprivation. You’re actually putting your body at more risk than benefiting from training under that little sleep.
I would look into DSIP (delta sleep inducing peptide), apeginin/magnesium L-threonate/L-theanine, cut all stimulants out (caffeine, nicotine, etc), maybe GH would help some.
More importantly, keep looking for a doc that will help you. That little sleep continuously will cause a wide array of long term health issues.
Make sure your room is cold (65-64°) there’s absolutely no light whatsoever, try a weighted blanket.
Honestly you’re playing with fire running gear, training, working, and sleeping that little.