The Ultra LSP 750 is actually closer to a 500 Watt PSU as far as the number of amps on the +12V rail go. If you only want to power one GTX 670 it might be okay. I would recommend that you go with a more reputable brand if possible. A 550 Watt PSU from a good brand like Antec, Seasonic, Corsair, XFX, or Enermax would be adequate, provided you have no plans to get a second 670 for SLI later on.
It varies, if the PSU works properly, it will just shut down and not damage anything. However, some poor quality PSUs will blow out if they are taxed too much, possibly taking other components down with it, which would be bad news if you have really expensive components like the GTX 670. The PSU blowing out isn't guaranteed to happen with the Ultra LSP750, but why take a chance when you have a $400 video card.