The broken http://fallout.wikia.com/wiki/Auto-Doc#Mark_III in Caesar's tent, can it be repaired and is it useable for anything?

It can be used later on in the Caesar's Legion quest line. But that's all I'm saying, I don't want to spoil the quest for you.

Without going Caesar's Legion route, it is just a shining example of the hipocrisy of Edward Sallow, of a kind typical amongst despots who think themselves exempt from the draconian rules they dictate.