No. The Spurs don't have any leverage. There isn't a point guard who is the caliber of Trae that is available. If they want to pair Trae with Wemby, they will have to pay. The Hawks do not have to trade Trae. This is a statement that is made only if Trae gets shopped, which I don't think will happen.
Memphis isn't trading Ja Morant, so there is really no avenue for San Antonio to get a legit star point guard like Trae.