Yes each server will recognize its own backups. Also as long as you don't overlap the backup schedules between the two you should also be fine. You don't want both servers trying to take snapshots at the same time.

I’m curious why you have two vCenter’s seeing the same datastores?  Actually, I’m kinda curious how.  I’m assuming that you have two sets of ESXI hosts attached to the same NFS mounts?  I would expect possibly corruption when using ISCSI or FC volumes because the hosts wouldn’t be cluster aware of each other since they’re in different vCenters, unless maybe you were using Enhanced Linked Mode, but perhaps NFS mounts behave differently?  I don’t have a ton of experience with NFS mounts to ESXI hosts except for the occasional NAS.

To Chris’ point, just don’t run backups of the same VM’s at the same time, but then I have to wonder if both vCenters have the same VM’s registered in both anyway.  Again, maybe ELM would have a play in here?  Interesting setup in my mind at least.