Note: I've never used mod_perl 2, but only mod_perl 1, so I'll refer to the version 1 documentation.

You can fork and send the mail from a separate process, but be careful because forking under mod_perl can be tricky. Or you can use a PerlCleanupHandler. http://perl.apache.org/docs/1.0/guide/performance.html#Forking_and_Executing_Subprocesses_from_mod_perl