Didn't he 'kind of' do a comic like this. I believe Dilbert couldn't log into the network and he was told to do various things by the IT guy that he couldn't do since he couldn't log into the network which included sending an email.... though I could be wrong. I've been reading enough of these strips that jokes are starting to blur together.
Makes sense. If the NETWORK is down, meaning the LAN, you will not be able to E-mail no matter what. I haev actually had something like this happen. A user claimed they could not SEND/RECEIVE mail, and they told the Helpdesk by sending an E-mail. We weren't sure how to respond without insulting the requester.
If the email system is on the LAN and the internet connection goes out, you can still email the IT/IS department for assistance. If the problem is not with your terminal, they probably already know about the issue. If the problem is with your terminal it is probably a bad NIC, switch, or an ID10T error.