PCI Express is all forwards and backwards compatible so it should "work". PCI express 2.0 has more bandwidth is the only thing. If that card is capable of saturating pci express 1.0, then you won't get maximum performance from the card. I don't know if that card is capable of saturating it though, honestly. Also, depending on what CPU you're using you might get a serious CPU bottleneck.
A 6670 is no where near capable of saturating PCI-E 1.0. Version 1.0 x16 is basically version 2 at x8.