Yep...sure can. No other changes are needed. Restore will be fine as long as you're using the same Repository. 

Probably a better way to do your Backups is to use a form of "container" object when selecting your VMs for your jobs. 2 containers are Clusters & Datastores, so it wouldn't matter what Host VMs are on. Another option is to use vSphere tags. 

Is the server within the same vCenter? If they’re managed by the same vCenter you should be fine provided you target the VM at the cluster/vCenter level.

Good catch Michael. I guess if Hosts are added individually without vCenter, there would be a slight issue there. 

Getting this error:

So if you added a new host to vCenter you'll need to go to the Inventory node > Managed Servers >vCenter, rt-click & rescan it. Then re-attempt to modify your job. 

Michael touched on it, and I can’t say I know the answer for a standalone host, but if the VM’s is moved between two different vCenter’s, then Veeam uses the MorefID and if the VM is registered on a different vCenter than originally, it’ll see it as a different VM and start a new backup chain.  That may not be all bad, but if you want to continue the same chain, you have to remap the MorefID so that it realizes it’s the same VM.  If you had two standalone ESXi hosts, then I’m not exactly sure what happens….I’m assuming it’s still not going to see it as the same VM but I’ve never tried and I’m unsure if the MorefID is vCenter specific or host specific when it’s registered.

That said, if you’re sending between hosts of the same vCenter, then you can target it through the vCenter and it won’t matter which host the VM is on.

Getting this error now after rescanning the new host

Error: The RPC server is unavailable.  RPC function call failed. Function name: :GetSvcVersion]. Target machine: :mx06bak01.cts.ctscorp.com:6160].     
Job finished with error at 8/28/2023 1:42:22 PM     
 

That’s saying you’re unable to connect to mx06bak01.cts.ctscorp.com on port 6160, check your network connectivity between your backup components

Another trick is edit the backup job and ‘re-browse’ to the object.

Sounds like some standalone hosts in the mix (not sure).

Please make sure the target ESXi host is managed by same vCenter Server.