The Hawks would likely agree to a sign and trade for Sheed's contract + a future draft pick.
Atlanta has luxury tax concerns so they are unlikely to be able to re-sign Childress themselves. Plus, they have very little negotiating power as result because nobody believes they'll match the offer sheet. So, a sign and trade to someone who doesn't have their MLE is a perfect scenario for Atlanta so long as they get something out of it (future draft pick).
I have no interest in Childress at this point in time though. I want to see if his game has improved over in Europe before committing $33 million over five years to him. I doubt it has improved enough to be worth that amount.