Two questions...
Do you have that option enabled in server-manager pannel?
If you mean "Forwarding address for administrative notices", then yes
Do you have any updates available and you're sure that server doesn't report them via e-mail?
Yes a whole bunch, which also leads to the question which repo's to have enabled for best/safest update option.
No, there is no email, but i am sure that at one point there was.... I have most likely broken it myself, so i don't report it as a bug.
Per