I may be late to the party, but there is a workaround that can get near what you want to do:
Type Win + Tab to show up the Multiple Desktops panel also showing windows of the current desktop. Clic droit on one of them and vous pouvez choose either "Show this window on all desktops" or "Show windows from this app on all desktops".
Vous pouvez now switch desktop and they'll stick to the screen.
Afaik, if you choose the 2nd option, it will remember your choice even if you close all windows from the app at one point.
hope it helps