The phone part does stay in contact with the network, but there is no exchange of data taking place.
Your email will be continue to be pushed to you unless you turn off Data Services. You can selectively turn it back on to receive your email when you know you have a good connection.
You are using a Wifi equipped model, does your carrier support Unlicensed Mobile Access (UMA)? If they do, you can avoid the roaming data charges by using it in a Wifi location.
Yeah, but I want to get email, given each one is around 20k, so I have to have data services on which is why I wanted to know if something in the background would be pinging servers for a reason.