Nah. It won't be stationary long enough to develop bed sores.
And actually, emus are very very well designed for sitting. Think about the male, who sits 23 hours and 50 minutes a day for seven-and-a-half weeks while hatching his clutch. (On grown birds, though, you will find a 'bald patch' on...
Ok. Deep breath.
First, from my experience with young injured emus, thrashing about in panic is a real problem.
That is, Emoo either sits despondently, staring at the wall opposite his/her little straw-filled box, or you try to move her/him outside, to get sun and air and a view, and she/he...