I have budgies and cockateils that chew newspaper and wallpaper, and they haven't been adversly affected by doing this. I try to discourage this behaviour (we rent so eating wallpaper is not good!), but when the birds are flying around the room while I am out, it's pretty hard to police it.
At the last place we lived it, I stripped the wall completely and repainted it - the landlords were very surprised because they didn't really care in the first place!
Live and learn!

My mum has a technique of placing thin cardboard in the areas where they pick at the wallpaper - this helps discourage them from eating the wallpaper and also gives them something to do as well.