Maybe.
But, Burks can and will play a lot of minutes at the "1". That'll free things up. Quote me on it.
I'm fine with that, but that still doesn't leave room for a top draft pick
SG Hayward 30 min
SF Carroll 28 min
SG Burks 15 min (with another 15 at the point)
SF Hood 23 min
total of 96 minutes.
All of those numbers are probably low for what each player should be getting and you are already out of minutes. My point is you don't have room for Carroll AND a top wing pick.
Here's some out of the box thinking that just might work. I know we all love Burks, but we don't know how he will fit in this system. He is a good scorer on a reasonable contract. If we knew we could sign Carroll for less, I think he would be a great option. Played for Quinn and loved it, already knows Utah, and great defender. Then trade Burks and #12 to move up to 6-7 range and draft Hezonja.
You get a better defender at probably a lower salary who would fit perfect, and you get your great shooter/scorer Hezonja.
Exum/Hayward/Carroll/Favors/Gobert. Possibly best defensive starting 5 in the league.
Burke/Hezonja/Hood/Booker/Tomic. Lacks a bit of defense, but they will be fine against backups, and have a lot of scoring punch.
Cotton/Milsap/Ingles/Motum (just cause he's australian) to fill in garbage time and for injuries