PCIe 3.0 should be backwards compatible with all previous revisions of PCIe, but, sometimes things happen. Once in awhile I do run into older boards running PCIe 1.1 that just won't work with 2.0 or 3.0 cards, but it tends to be the cheaper boards with early implementations of 1.1.
That aside, a 720 should work perfectly fine in such an old machine as long as your not planning on gaming.
Why put a performance card in a 8 year old system? That board supports Core 2 Duo or Pentium D CPU chips. And it runs DDR2 ram. GIGABYTE - Motherboard - Socket 775 - GA-945P-S3 (rev. 3.3)
It's not about the PCI-e slot or how many lanes the slot has or if it's backward compatible. It's about how slow that system is. I think you're about to be sorely disappointed.
CPU chips it can handle. N/A means it's not supported.
GIGABYTE TECHNOLOGY Socket 775 - Intel 945P - GA-945P-S3 (rev. 3.3)
Memory it can use. Notice at the top it says DDR2 667.
http://download.gigabyte.us/FileList/Memory/motherboard_memory_ga-945p-s3_3.3.pdf
Well, the pins are the same in all PCI-E x8 and x16 standards, and they are pretty much the same across the board, the only real difference is the bandwith of the bus, which even on 1.1 is not going to be saturated (there is still a lot of headroom in terms of speed between PCI and CPU even on 1.1 I mean, the bus is faster than the components at each end)
There's always a bit of risk involved when putting newer stuff in an older system. If it was me doing this, I'd just go for it and see how I got on since after reading up a bit I'm pretty confident it would work.
do let us know how it goes if you bite the bullet, im always interested to see how things like this pan out