Yes, they do.
And what helps Utah with Burks (and Hayward) is that they will be RFA's. Utah can match any offer and likely will. Jazz are in great financial shape. There aren't (or rather, there won't be after this season) any bad contracts. We won't be paying washed-up vets exorbitant salaries. Hayward and Burks aren't superstars. They'll probably draw some interest - and Lindsey may even tell them to go out and see what their market value is if they don't like Utah's offer. But in the end, a team making an offer has to clear - and keep that cap space available - if they were to sign either to an offer sheet. And they'd do that knowing Utah could, and probably would, match.
This a much different situation than Matthews. Portland knew matching their offer would put Utah into the luxury tax.
I agree with with Cy. It's highly unlikely Alec would get $12M. I see Hayward ultimately signing for about the same as Favors. Justification will be that he's not a big, but he's obviously a more integral part of the offense. Burks IS going to blow up next season as a starter or as a 6th man. Be prepared for him to get $8M or so. I predict the Jazz will eventually move Kanter. Back-up 5 mins will go to Gobert and Lindsey will draft or sign another PF to pair with Marvin (yes, I do think he'll be back with the Jazz next season).