Technically, if you'd block IE, some applications might fail because of this, even if they don't connect to the Internet. IE has become a core part of the Windows operating system and it's becoming more and more important these days.
Then again, your problem seems to be the users who connect to the Internet for reading their emails and probably for some other personal stuff. Is this bad? It happens so often at companies that it has been investigated and as it turns out, it tends to make people a bit more productive if they can use IE and email at work. One reason for this is because it keeps them connected to their computer instead of wandering off to colleagues for a quick chat. So if you don't allow IE and OE because you fear that you'll lose productivity, then you're wrong.
About security... You can't really block applications at the router level, although routers are able to detect communications from certain kinds of applications. Such a browser might block IE but still allow Chrome or Firefox. Which brings me to an interesting alternative... Why not install and enforce the use of Chrome or Firefox on those computers? It will be a bit more secure. If you also want to provide an email alternative, get Mozilla's Seamonkey, which combines browsing and email in one product. Then users might not use IE and OE anymore. (Then again, something as simple as a Windows update might bring it back again.)
And install a good antivirus product on those computers, just in case. Blocking IE and OE won't keep them secure since there are many other ways that can infect a computer. MS-Word is already known to be insecure and so is Acrobat Reader. A bug in the Windows GUI even made simple JPG images a potential hazard but this has been fixed in one of the updates.