No, screen sharing is deactivated by default when you join a CoScreen. You are always in control. Just click on the disabled screen-sharing icon next to your user once you are in a CoScreen to share your windows on this display.
Please note that CoScreen does neither share your desktop background nor the icons on this display. It only shares the windows that are open on that display if you share any windows. And unlike in other screen sharing solutions, you can share multiple individual windows at once and they are all marked with a colored border so that you know that you're sharing them.