Is there a way to get Perforce to send you an email on every check to a particular depository?
You want to install the Perforce Review Daemon script on your server. What it does is periodically poll the server for new changelists and sends an e-mail ONLY to the people interested in them. The script is maintained by Perforce and you can get help from the tech support to setup it.
You can download it from the Perforce website from the support site (towards the bottom of the page).
Perforce Support Site: http://www.perforce.com/perforce/loadsupp.html
Direct Link to Script: http://public.perforce.com/public/perforce/utils/reviewd/p4review.py
Once you have it installed you register your that your interested in changinglists by adding the filespec to your user account.