I definitely think adding Butler/George AND someone like Noel to the team would make us contenders, but not just Butler/George alone. We're not a true contender with Amir as a starter.
Let's say the trade for either George/Butler is Zeller (salary), Brown, Young, and the two Brooklyn picks.
Let's say the trade for Noel is Rozier and the Memphis pick.
That'd leave you with the following roster:
PG: IT, Smart
SG: Bradley, Green
SF: George/Butler, Crowder
PF: Horford, JJ
C: Noel, KO, Amir
That's definitely a championship-level roster.
A less ideal scenario is the Bulls/Pacers demanding Crowder/Bradley rather than the 2018 pick, but we're still a contender in that scenario I think. So let's suppose the trade would be Crowder, Zeller, Brown, and the 2017 Brooklyn pick for George. I'd try to get Miles back in that trade, which shouldn't be a deal breaker, and that'd leave us with:
PG: IT, Smart
SG: Bradley, Green
SF: George/Butler, Miles
PF: Horford, JJ
C: Noel, KO, Amir
That's still a championship-level roster.
EDIT: And iirc, the rumored trade value for Butler that Chicago wanted from us at the draft was the 2016 draft pick (which turned into Brown), Crowder, and the 2017 pick. I think you have to do that deal today if offered, as long as you have another upgrade in place for Amir, such as Noel.