Yes PCIe spes are backwards compatible. Often though when a new spec comes older boards get bios updates that help that compatibility so you may want to see if your board has an update to the bios if you have trouble. That may help a lot.
There are issues with PCIe Gen 4.0 GPUs on AMD CPU systems. Symptoms include integrated audio issues and USB issues (mouse stuttering, webcam glitching, disconnects/resets). If you run into issues, set PCIe to Gen 3.0 in the BIOS.
