Hi Paul, the short answer is Yes. However, you can probably connect for a very short time, just to download and send, and then go offline to read it all on your own computer. If however, you are accessing web-based emails through a browser (i.e. Hotmail), you'll have to be connected continuously.
If you're travelling and want to avoid big data roaming charges, try and find wi-fi hotspots or see if there's a local pre-paid sim-card option. There's quite a few other Q's on this site about this.
See: http://answers.worldnomads.com/search?q=sim-card&commit= almost 7 years ago