Technically Outlook doesn't support the .pst database on a Network Share however I've done it for years on normal Windows Networks and with the exception of normal network communication issues that can come about haven't had and issues that would stop me from continuing to do it however I do maintain a sync with a PIM as well as daily backups of my .pst files and am properly prepared to minimize data loss under the circumstances. That said however I would not use VMware Shared Folders for that nor recommend it for the average user. What I'd suggest is leave it on the local drive under Windows and backup the .pst files outside of the Virtual Machine to the Host or NAS, External Drive, USB Flash Drive, etc. This can be automated many different ways to make it easier.

Not to put words in Woody's mouth, but the way I read his response it sounded like I think Woody was suggesting while it isn't supported by Microsoft he's been doing what you're asking for for quite some time.

That said I wasn't aware it wasn't supported and have my PST files on the \\.host\Shared folder for a bit now without any problems as well. I haven't tried putting my OST file there yet.

I made a copy of my PST files to the shared folders, changed the config in Outlook to the correct directories, restarted Outlook and after I checked everything, deleted the original PST files on my local drive.