Most window managers allow the user to "iconify" a frame, removing it from sight, and leaving a small, distinctive "icon" window in its place. Clicking on the icon window makes the frame itself appear again. If you have many clients running at once, you can avoid cluttering up the screen by iconifying most of the clients.
Use a picture of a gnu as the Emacs icon.
Start Emacs in iconified state.
The -i or -icon-type option tells Emacs to use an icon window containing a picture of the GNU gnu. If omitted, Emacs lets the window manager choose what sort of icon to use--usually just a small rectangle containing the frame's title.
The -iconic option tells Emacs to begin running as an icon, rather than showing a frame right away. In this situation, the icon is the only indication that Emacs has started; the text frame doesn't appear until you deiconify it.