Is it possible to send an email from FMS? If not, how would I go about creating
a connection from FMS to a http server running PHP? Just use LoadVars like a
regular Flash client? Would that invoke cross-domain issues to resolve?

FMS isn't a mailserver, so it can't send mail directly.

You can connect up to your php server using LoadVars. You can also use
netServices and AMFPHP, but that's probably overkill for your purposes.
Loadvars on the server side is pretty much the same as loadvars on the client
side. There is no sandbox for FMS like there is for the Flashplayer, so the
cross domain concerns don't apply.