You could try spraying the naked foam with 3M spray adhesive, and then applying the tape. Of course it would probably be very unforgiving. One touch and it's stuck. Of course I haven't tried this myself, so let us know what happens if you try it.
In humid climates, tape actually sticks better than the paper. Just need to carefully allign, smooth on firmly and overlap strips.
As for strength, it's a little weak in big peices fully nekkid, but good in small or laminated peices.
Biggest downside of bare dt foam is it's low tolerance for abrasion. It'll gash if you just look at wrong. A layer of tape/contact paper/glued coffee filters/polyurethaned glass cloth will help with that. One side is ok for a wall, but make sure every exposed side is covered with something.
This doesn't answer your question directly however, I came across this guys videos making wings and planes out of foam board. He covers or paints the foam board. See link: http://www.youtube.com/watch?v=qJZoqGHAIDE