I'll take a dump in the woods and though I generally try to do it as far away as possible from where I'm hunting, I did once take one right beside the spot where my old man later came and sat and he had a magnificient buck still come right out to him later that morning (I didn't mention what I had done and I did cover with leaves and dirt). I've also pissed off the side of my tree stand and still had deer come out, so there you go. Not something I want to do, but when you have to go, you have to go.

Incidentally, I usually carry TP, but if I forget, the correct order of sacrificing your clothing is t-shirt sleeves, t-shirt itself, underwear, socks.