That is indeed possible.
When you open the Overview screen, you get a small "board pin" icon, next to the Overview link. Clicking on this, makes the Overview page, default.
The same applies for other links on the Home screen(Inbox, Actions, Activity).
Naturally, if you have an overview page, it will be the default starting point for users. They can however change this by "pinning" another area as a starting point (ask Mandar mentioned above)
I think you're asking from the perspective of the owner of a group or space, how to ensure all users see the Overview tab by default, instead of the Activity tab, right?
After much digging I figured this out:
1. Click Manage > Settings
2. Click the About button (right hand side)
3. You get a dialog. Select Advanced Options at the bottom
4. If you select to enable both Activity and Overview page, it will allow you to select which is shown by default.
Hope that helps,