I don't see why not, as long as it's an AGP graphics card, not PCI-express. I think the real question is whether your power supply will be able to handle it.
What are your specs? just give a rough guideline if you're not sure what you have.
The specs looks fine to me, with the exception of the PSU. I don't think 300W will be enough for one of those 6800GT monsters, you're gonna need a new one. Apparently, and I'm no expert on this, you should have at least 24 amps on your 12V rail; you should find these specs when you look at PSUs on various retail websites. As long as you get a decent brand like Antec that is about 400W or more, you should be ok as these ought to have enough current on the 12V rail by virtue of being good PSUs.
There are plenty of people here that know an awful lot more about PSUs than I do, hopefully someone will post about it. You could also try looking through the forums for other posts about PSUs.
Yeah, the 6800GT requires additional power so they come with a molex adapter (or whatever you call those power cables). Can't remember exactly how much power it requires, but it's somewhere in the region of 65-85W.
I've heard it is best to have a 500W PSU with the 6800GT. I've got a 6600GT with a 450W PSU and it works fine but doesn't have the molex power connector. If you install a 500W PSU, you should be good for a few years. Just look for a quiet one, it'll be more expensive but well worth it.