There is no correlation between screen and a windowing environment ("window manager"). No matter what form of windowing manager you run, you can still run screen.
The question then becomes what lose/gain by moving away from a desktop environment to a windowing manager. What does a desktop environment give you:
- Standardized programming interfaces for apps (from Gnome and KDE) to integrate with the environment.
- Notification systems
- Integration with display manager (gdm, kdm, lightdm, lxdm); automated starting of environment.
- System tray (window managers can include, but are more like "task lists" than real system trays) and other add-ons.
- Better integration with settings managers to automated settings up the environment.
For a list of Window managers, look at http://xwinman.org/. When you have chosen which system to work with, then you will need to figure out how to start the system (for the most part it is the same, but each window manager has their own convention).
Desktop environments all have a window manager running underneath so you could still choose a different window manager and keep your desktop.