We have two hosts set up for HA under 5.5 Essentials Plus.
The vCenter server is a VM on one of the hosts. If the host with the vCenter server suffers a hardware failure, can the lost VMs start on the other host or are we out of luck?
HA works independently of vCenter Server. vCenter Server is only required for the configuration, the HA functionality is on the ESXi hosts.
As long as the vCenter Server is stored on shared storage, it will be restarted on another host in case of a failure like any other VM
So, while HA, by design, will respond to failures without vCenter, HA relies on vCenter to be available to configure or monitor the cluster.