My guess would be that this would work, but could potentially run into speed or compatibility issues. My opinion would be that in terms of risk-vs-cost, and potential waste of time/money, it would make more sense to either swap the mobo or graphics card.
Note that the adapter card itself is plug-and-play compatible which means it needs to load windows drivers to work. Since a video card is an output device, it would have a better chance of working than something like a NIC, since the faster card would have no problem keeping up with the slower PCI bus.
Below is from http://www.directron.com/expressguide.html
Common Buses and their Max Bandwidth
PCI 132 MB/s
AGP 8X 2,100 MB/s
PCI Express 1x 250 [500]* MB/s
PCI Express 2x 500 [1000]* MB/s
PCI Express 4x 1000 [2000]* MB/s
PCI Express 8x 2000 [4000]* MB/s
PCI Express 16x 4000 [8000]* MB/s
PCI Express 32x 8000 [16000]* MB/s
USB 2.0 (Max Possible) 60 MB/s
IDE (ATA100) 100 MB/s
IDE (ATA133) 133 MB/s
SATA 150 MB/s
SATA II 300 MB/s
Gigabit Ethernet 125 MB/s
IEEE1394B [Firewire 800] ~100 MB/s*
* Note 1 - Since PCI Express is a serial based technology, data can be sent over the bus in two directions at once. Normal PCI is Parallel, and as such all data goes in one direction around the loop. Each 1x lane in PCI Express can transmit in both directions at once. In the table the first number is the bandwidth in one direction and the second number is the combined bandwidth in both directions. Also please note that in PCI Express bandwidth is not shared the same way as in PCI, so there is less congestion on the bus.
Update: Table above contains speeds for PCI Express 1.0 bus. For version 2.0, multiply all bandwidths by 2. For example a PCI Express 2.0 16x slot has a max bandwidth of 8000 MB/s one way or 16000 MB/s both ways.