No. All my apps and windows are on one desktop space in the UI.
For further testing, I tried another file as well as a totally blank new file. Went into the animation workspace and then entered full screen mode via the icon for "Fullscreen Mode for animation playback" at the bottom of the window. Then then exited fullscreen, once by hitting the escape key and once by clicking the icon in the bottom right of the screen to return to normal view. Both times I was unable to interact with Fusion 360 after returning to normal view; it wouldn't react to any mouse clicks or key presses. But when closing Fusion 360 via the dock icon, the save dialogue box popped up if there were any unsaved changes, however it wouldn't respond to clicking any option to save or not. Just like described by esopher above. I also tried another way to exit full screen by clicking the green circle at the top left of the top menu bar (it drops down when moving the mouse to the top of the screen in full screen mode) and had the same unresponsive result.
However, if I first make Fusion 360 fullscreen by clicking the green circle at the top left of it's window and then enter the "Fullscreen Mode for animation playback" by clicking that icon at the bottom of the screen, then I can exit full screen by any of the methods listed above and Fusion 360 remains functional and responsive.
So entering "Fullscreen Mode for animation playback" from a window of Fusion 360 causes it not to respond when leaving fullscreen. But doing it when Fusion 360 is already fullscreen doesn't cause any problems.
Does that make sense?