As mine was a carnivorous plant terrarium I had to use peat, I mixed a little perlite in and sat that layer on top of the false bottom, then topped off with pure peat to hide the perlite.
Regarding the peat on background: I wouldn't have thought so, though I'm not entirely sure. Peat is often used in Killifish aquariums to lower the pH of the water to a more natural level; I don't really think a small amount of peat would cause any trouble but again, I don't rightly know. I would have though that, with a layer of soil over the background, the water could climb up and be absorbed by the peat but I've not had any experience with soil covered backgrounds so I really am not sure. Ever so sorry. If you google "reptile forums" you should find a swathe of information about people who've used this method for their reptile and amphibian enclosures.
I hope you'll detail your progress when you start!
It'll be brilliant!