CharlesGrey: I figure worst case you'd end up with system instability, crashes, or it would refuse to start up at all, as you say. I don't think underpowering ( unlike supplying it with too much power ) would actually break the GPU. Still, I agree that it's best to remove potentially broken components right away, to protect the rest of the system.
Navagon: I haven't done it myself, but I've read it can happen. But, like I said, your system would beep like a madman and refuse to boot if there were inadequate power rails attached. So this pretty much remains a hypothetical for me as it almost can't happen without the safeguards being removed.
My guess is that jefequeso's card is so comprehensively fried that it's not even recognised as a GPU any more and that's why he can boot in this state. The problem with that is there's no way of knowing if it's going to have a negative impact on other components in its current state.
Nope, that is not correct sir/madam. No beeping, no harm done to any hardware, you would simply get a warning message in Windows. I do this all the time as part of my job.
Take a look at the PCI-E specification if you are interested in the technicalities. When the card powers on, it negotiates with the motherboard how much power to draw. If external power is not connected, the card easily detects that, powers down most of the hardware components, boots just fine, and Windows warns the user with a nice pop-up alert. You can still use your computer, surf the net etc., but absolutely no 3D acceleration or performance.
But... if you connect power from a defective PSU, which doesn't supply what it says it does for example, that could of course harm the electronic components.
To the OP: Enjoy your new toy :)