I think it's a good fight,
Elder Centipede is extremely big, probably the biggest monster, which was an issue so even Saitama used Serious Punch to one-shot it.
Homeless Emperor's offensive powers are very unique, but he wasn't able to penetrate Tatsumaki's defenses, will that be enough to finish Elder Centipede? Not sure, maybe.
Homeless Emperor has one major weakness, he is just a regular guy who is using limitless Energy attacks, if people can get close to him and catch him, it's over. Even Zombieman, who is nothing to Dragon level opponents, was able to defeat Homeless Emperor by catching him off-guard, even with preparation, Zombieman is just an insect to Elder Centipede, he can't do anything to it no matter what.
If Elder Centipede goes underground, and suddenly appears from under Homeless Emperor, he might one-shot Homeless Emperor, but not sure if Homeless Emperor has enough power to hurt something like Elder Centipede, who resisted to Metal Knight's missiles, and Bang's + Bomb's + Genos's combined attacks, can Homeless Emperor surpass their combined attacks? Surely, his attack power is superior to them one by one, but collectively Bang + Bomb + Genos vs. Homeless Emperor's attacks, it shouldn't be a big difference although Homeless Emperor probably still can produce better attack power than them. But not sure if it will be enough for something as durable as Elder Centipede or not.