Will be the limiting factor. The Corsair MP500 can hit up to 3000 MB/s in read (lower in actual use), but PCIe 2.0 x1 will go nowhere even remotely close to that. A plain SATA 6 Gbps SSD will be cheaper and probably be just as fast as a PCIe 2.0 x1 drive.
Would it work? Probably not. The crosshair Z (and AM3+ as a platform) are old, and probably don't support booting from an NVMe drive. That support has to be implemented into the bios, and glancing through the bios updates page on the Asus website, I don't see a mention anywhere of adding NVMe support. That means you could use it only as a data drive, not as a boot drive.
Then there is the factor a x1 pcie 2.0. A pcie x1 2.0 actually has lower bandwidth available to it than a Sata 6Gbps connector. Sata caps out (theoretically before overhead) at about 600Mbps, while a x1 2.0 slot only has 500Mbps available (before overhead so you won't actually even achieve 500Mbps on this). You'd be limiting that Corsair MP600 to less than 1/6th it's possible performance, and wouldn't be able to boot from it. If you move to a pcie 2.0 x4, you could get close to half (and still not able to boot from it).
So in summary, yes it would have a massive impact on performance, no you can't boot from it, but yes you technically could use it as a program/data drive even though that would be a massive waste considering the massive bottleneck of a x1 slot.
Upgrade your platform before you upgrade your drive
Hmmm. Well thanks for the information though I was really curious to see if it would actually be something viable for an older platform. I think I'll just use the Corsair 500 in my x99 rig and use the drive I currently have in there as the boot drive for this Linux rig since it's a sata SSD because that makes away more sense but I was just asking that stuff out of curiosity but I'm looking to upgrade to Ryzen soon with the Asrock x370 taichi, Ryzen 7 1700 and some Gskill RAM at 3200.