From my experience, the fan has to be out of the way to get the shroud out. That was on my 88 F-250 I did a few weeks ago, and ages ago when we did the water pump in our 85 Gasser E-150.
However, I did find on the brick, you can remove and reinstall the fan/clutch with the shroud on. I just grabbed the tips of the blade, and un-threaded, or threaded the fan on. I even dealt with all the belts with the fan/clutch off. Made it much nicer to fiddle with the belts.
The only Ford fan shroud that I know is designed to be removed in two pieces (this is personal experience) is on a 6.0. They are installed as one piece from the factory, but they are marked and have holes in them to cut and bolt back together. But, a 6.0 shroud is much deeper than an IDI. It's difficult to even see the belt and accessories. Even replacing the belt is rough......