It probably would depend on the density of the foam. For example, Schluter has a foam shower tray. You don't tile to it directly, but you do after installing their waterproof membrane, Kerdi. I used one of their pans when I did a remodel at my Mother's house and it works fine. You may want to consider maybe Ditra directly on the foam, but I'd call Schluter first. Also, at least with their foam tray and curbing, it is designed to be thinsetted to the subflooring. If you did the whole floor except the shower area with sheets, then used their pan for the shower, you might be able to build a curbless shower if you used Ditra outside of the area, and used the Kerdi-band on the seams to waterproof the whole thing.
Call Schluter and run the ideas by the people at www.johnbridge.com. Should be interesting.