Patsas (Tripe soup) is a Greek hangover cure specialty. It occupies the same niche in Greece that a late night kebab occupies in Britain.
The answer is, not really; Stalactites would be the obvious place to do it (one of the few remnants of the original Greektown in the CBD, which is open 24/7); but I don’t see it on their menu.
One of the places in the current Greektown, Oakleigh, does offer it: Yefsi. But Yefsi closes at 10 pm.