Right now, logins via gdm don't set MAIL or MAILPATH at login. shadow won't either as of version 4.0.15 or thereabouts (per a conversation with SpanKY--the fact that it sets them today is a bug). So it looks like the right thing to do is for the user to set MAIL or MAILPATH and MAILCHECK, if they want their shell to notify about incoming mail. It would be nice to have these environment variables listed in the docs on nifty and interesting environment variables that a newly-installing user will want to know about.
No need. We already talk about setting those values in the various mail guides, like mailfilter and guide-to-mutt. Whether or not GDM or any other login manager sets them is irrelevant.