Can High Availability still work with different CPU versions regardless if all cores are the same per host in the cluster or different from each other?
High Availability is the restart of a virtual machine on a different host within a HA cluster, so doesn't need to be identical CPU as far as i know.
Design best practice would suggest each node of the cluster would mean each host is near identical, same cpu version and family (but maybe different speed / cores etc).
Check out the vSphere High Availability (HA) Technical Deepdive - Yellow Bricks by Duncan Epping
HA will still work even with completely different CPUs between your physical hosts. You could even mix AMD and Intel CPUs, though I certainly would not recommend this.
This is because HA does not rely on vMotion (DRS does) to perform live migrations, HA is just a re-power on operation from a hard powered-off state (think plugging the power cord).
This begs the question of why you don't want to use live migration on your clusters. Remember, HA has the same shared-storage requirement as well.
Agree with the others, it should work regardless.
HA will work. if using different CPU families in cluster then enable EVC mode for compatibility.