The short answer is Yes. The long answer is mostly yes, all games support alt tabbing, obviously (so you would be watching for emails on the other monitor, and minimizing the game to respond).
The holy-grail for multi-monitor support in games is a setting called "Windowed-no-border" or "Full Screen Window", where the game essentially creates a full screen window without standard windows borders. Depending on the game, you can freely leave the game with your mouse, or alt tab from the game without it being minimized. This way, you don't have issues from minimizing and restoring the game, and you will still see the game window while responding to email (unless you move a window over it).
Support for this option is becoming more common in games as multimonitor becomes more common, and it's especially common in multiplayer games.