Yes, a new PCIe Wi-Fi card can function on PCI x1 2.0.
Yes, a new PCIe Wi-Fi card can function on PCI x1 2.0.
I'm searching for that specific card from the provided link. Your PC supports PCIe x1 but not version 3.0, and you're asking if the available bandwidth is sufficient.
PCIe 2.0 x1 delivers 500 MB/s of available speed. The Wi-Fi chip claims 3000 Mbps, which matches about 375 MB/s. That should work fine.