You can pull the log using OMSA - managed node from the OS (although you are likely running too old a version of ESXi to run the OMSA VIB) or an OMSA live disc.
Yes it is, but probably just not the latest Support Live discs. Looks like the older versions (like 5.1-6.4) versions have been pulled again.
Chris or Daniel ... you guys have the pull to tell somebody to put the older OMSA live images back up?!
You could do a CentOS 5.4 (or even 6.4), then download and install OMSA manually (OMSA Live is just a CentOS live disc with OMSA and Online Diagnostics pre-installed and ready to go). Since you are just after the logs, you could probably pull the "tty" logs from any Linux live disc.