If I'm expecting something critical I either manually check e-mail or turn the action off. Surprisingly it doesn't bother my Google Talk notifications so I'm assuming they're coming over on 3g data?
Well if it turns off wifi and data you shouldn't receive anything. It doesn't matter if it's a 4G or 3G connection, a data connection is a data connection.
And yeah... that doesn't sound too hot to me. I like to be able to glance at my phone to see if I have new email and to be able to hop on the web as soon as I unlock it instead of waiting for it to make some type of connection. Hm.