Is a direct LAN access to the ESX server required from the HBBU proxy server. Connection to the Virtual Center exists already.
If the backups are being taken via the Virtual Center (VC), then its sufficient that the user has LAN access to VC
If the job is submitted at the VC level, then the LAN access to ESX is not required.
The logic is that while submitting the job, if the user selects the VC, then the connection is established with the VC first, and then the VC connects to the corresponding ESX server.
Other points to note:
For Hot Add mode, the HBBU proxy machines should reside on the same ESX server from where the user is backing up the Virtual Machines
For SAN mode backups to work the HBBU proxy machines should have access to the SAN LUNs, where the virtual machine's VMDK files reside