I would guess that since Microsoft doesn't even support a PST placed on a
mapped network drive that perhaps an FTP server wouldn't be such a good idea.
Is it possible? Yes. Would it work well? Possibly not and because it's not
supported or recommended, you would have no recourse if anything went wrong
and you didn't keep a good backup.
Outlook needs to have read/write access to the PST which works best when the
PST is kept locally on the PC.