Interestingly, today a colleague of mine asked me this question.
He wanted to know what would happen to vCenter if it was situated on a site that went offline unexpectedly in a Stretched Cluster setup.
The answer to this is pretty obvious- vSphere HA would restart all the Virtual Machines from the offline site to the other site and it works the same for your vCenter Server Appliance (which is also a VM) as well.
Let me explain a little more.
vSphere HA works independently from vCenter. You do not require vCenter to be up and running in order for HA to work. Of course, with that being said, while vCenter is not necessary for vSphere HA to work, HA is still dependent on vCenter during the initial installation and configuration phase.
What this means is that even if vCenter is down/unavailable, vSphere HA would still work. Unlike what some of us thinks, vCenter does not trigger the HA event. It is the small, lightweight agent running on each ESXi host called the Fault Domain Manager (FDM) that does the triggering.
The agents on all the hosts talks to each other about host resource information and VM states in the same vSphere cluster. Because of this communication, if in the case of a failure, the agents would trigger the restarting event and the VMs would restart onto another healthy ESXi instead.
Hence, when vCenter is situated on a site that fails/goes offline- vSphere HA would kick in and restart it to the secondary site. So all is good!