It shouldn't make any sound when you get an email if the "notification" slider is all the way to the left.
Test it like this...press up on the volume button at least two times, then press the gear symbol that appears to see the four volume sliders. On my phone, starting from the top down, these sliders are ringtone, media, notifications, and system. With your finger, move all of the sliders to the right, then wait a few seconds for the menu to disappear. Then press and hold down the volume button until the phone vibrates. Again, press the gear symbol to see the volume sliders, and you should see all of the sliders have move to the left except the "media" slider.
On my phone, this turns off the notification sound for almost everything including the stock G-Mail, Email, calendar, and text messaging apps. It does not turn off the sound for any alarms that I have set in the stock clock application.
