If the power supply is good quality, then it'll turn off if the graphics card uses too much power. This will generally happen when you're running a demanding game and the graphics card is in full gear for a while. Note that this doesn't happen when booting, only at full load.
If the power supply is bad, then all kinds of things can happen. Generally if the current is enough it'll work But if there is a power outage etc or something like that, the PSU may go out.
The power supply you linked is really only a 360W power supply. I wouldn't try to run a 151W card on it. Personally, I don't think you should chance it.
That's the tradeoff- since you're getting the GPU second hand(and it's nowhere near a weak one I'd say) you have to spend some decent money for powering it.