I am convinced they do ! It was only a fortnight ago when my other half (Chris) saw Gizzy eating invisible crickets in her sleep lol. He said she spent 2-3 mins chewing away.
I KNEW IT! hahhaa, last night i was lookin around the obamas cage while he was asleep and i noticed he was all fired up with his eyes closed and mouth was actin like it ate somethin, i thought he had a midnight snack for a minute! hahahaaa