I don't expect that the Celtics will necessarily trade anyone directly in response to signing or not signing Walker. I think what has to happen is that Walker has to prove he can be a rotation player, at or near the Pritchard/Hauser level. If they think he is that good (based on preseason performance), he is worth signing. If he is less than that, maybe more at the Mykhailiuk or Stevens level of expected contribution, then they probably don't sign him.
I think the hope or even expectation is that Walker will be able to play at a level of #9 or #10 on the roster, right there with Pritchard or Hauser. If not, there is no reason to pay him. I am not sure where he will fit but it seems realistic that he can be right there with Pritchard/Hauser.