You can put the hash in the blockchain and prove it was taken before that block was generated. It would be good proof to me, but proving the timestamp of that block and what your hash proves would likely be "interesting" in court. That's a lot of math you'd have to explain to a jury.
Courts have "experts". You just need one that understands bitcoin and can testify that he knows that including the hash retroactively isn't possible. The other party's expert won't be able to claim otherwise without perjuring himself, and any math teacher or computer science professor from a local college will be able to back your guy up on the tricky parts (hashing), even if he doesn't know bitcoin specifically.
Oh, but keep in mind that the timestamps aren't exact. There is a several hour window on either side. That is enough for most things, but not enough for precision timing.