The browser object uses the "blur" action to suspend it (and the "focus" to re-activate it), its not effected by the layout timescale.
Strangely, when I have the timescale paused, the browser object doesn't switch back when I have a 0.2 second pause to allow it to change the scaling mode before it goes back to fullscreen. It works using delta time, but it's buggy and gets stuck on scale inner (I have to blindly switch modes again before it shows up again).
EDIT: After further testing, yes, using delta time to switch scaling modes and changing disabling fullscreen to reenabling fullscreen (to allow the change) doesn't work. The switch works fine with 0.2 second game between the switch and timescale at 1.0, but doesn't work properly with timescale set to 0 and using delta time.