As Marshall Goldberg notes, at best, nothing will happen. With most AV setups there's a source like a computer, video camera, etc. This is where the signal starts from. It goes in one direction and arrives at a destination, like a TV, projector, etc. Usually the signal is a one way deal, which is why connecting two computers won't do much.

HDMI does have a little bit of two way communication because the devices do an HDCP (High-bandwidth Digital Content Protection) handshake to make sure the receiving device won't allow for easy pirating. But both computers are sources, neither one is a destination so they won't be able to send data.

I'd guess there's some peripherals you could buy that connect to a computer and allow processing of the HDMI signal, but generally if you're looking for flexibility you're better off getting a source that will send SDI, or DVI, since it doesn't have HDCP.