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 their lower chest if you slide your hand down. I've always assumed it's from roosting at night.)
Spinach and dandelions and 'brikets' -- which I assume is dry food from the store -- is a good mix for an emu.
My project here -- 'Planet Rothschildi' -- exists because the house-clearing around my old farmhouse is a source of treats for emus: plums, figs, apricots, pears, grapes, lilly pillies. They never get junk food. It's a rule.
I mention this because it's taught me about 'treats'. Emus don't seem to like citrus. But otherwise, they'll scoff down absurd quantities of fresh and dried fruit.
And I wouldn't worry about Emoo overeating. We've never had a post about a fat emu. (But pet emus need, on average, far more exercise than they seem to get!!) It seems to be that they'll gobble up an amount. Then, when quite full, just stop.
Below is Felicity Emu scoffing Cape Weed flowers. Felicity luuurvs these, and use to come back from her travels every spring to enjoy them.
More importantly, perhaps, is that healthy treats are a way of giving her/him some attention while she/he is out of action. No one wants their emu injured, but time invested is the Nos. 1 aspect of taming emu chicks. Ultimately, the adult bird will be able to be handled for medical inspections and treatments. I can't do this for 'my' birds -- which aren't mine; they're wild -- and it's always been a problem.
Supreme Emu, Lake Muir, Western Australia