I'm actually inclined to think Ainge would take back Lou Williams to keep ATL happy about giving up a pick or Schroeder.
Nope -- the whole point of Ainge dealing Green is to clear his salary. You basically have Ainge paying $5.5mil next year (Williams salary) for a pick around 20... when he already has picks. The flexibility is more valuable.
Presumably Ainge's goal is to get two pieces: a) an expiring contract, and b) either a pick or a young player on rookie contract (for the sake of argument here, Schroeder). I also presume he's only gotten half that offer yet... the expiring... or Green would have been traded already, just as Courtney Lee was.
Ainge knows offers will likely improve a little before the deadline, so he'll wait and see if he can squeeze out a pick or a rookie contract player before the deadline by shopping the Hawks (or anyone else's) offer around to other teams to see if they bite before 2/20.
If not, I bet he'll ship Green for the expiring alone.