Simply turning beta channels on will not put you into a beta, if a beta is available. To select a beta build, you have to do the following:
1. Go the the installed game.
2. Click MORE -> Settings.
3. Turn Beta Channels -> ON.
4. Under the channel drop down menu, select beta (or whatever the beta update is called). Default is the default channel or main channel, this is the channel for released (non beta) updates.
5. If the beta is non public (ie the beta has a password), select add private channel and enter said password. Most beta's will be public.
I don't own EE so I can't check if a beta is avilable, but you should see it listed under the channel drop down menu under default if there is one.
InkPanther: Are you asking about Galaxy or Steam? I'm not using Galaxy, but I've never heard about "beta channels".
Beta channels are a Galaxy feature, and as it sounds... they are simply unreleased beta builds that you can opt into to test buggy features or content before official release.