Completed the upgrade to vCenter v5.5 Update 3e yesterday and there were only some minor glitches in the initial part when upgrading Single Sign On (the installer reported certificate problems, however this seems to have been a false-positive, as after investigating I decided to proceed with the upgrade anyway, trusting in my Veeam backup and a VMware snapshot to bail me out).
Some additional good news: I had been getting an SSL/TLS error in the System event log on my VBR server (Event ID 36888) every time a backup was run. Backups were working fine, but it was a bit disconcerting. After the upgrade to vCenter v5.5 (and presumably new self-signed certs being created?) the event log errors are gone.