Not if they follow the rules. If the don't sign and trade, use the MLE or BAE... they don't get hard capped. That's it. So they can sign their players with bird, early bird to max contracts, early bird rights to 175% of their previous salary and non bird rights to 125% of theirs and go as far over the salary cap as they please and have a taxpayer MLE every off season.
If a team had 14 players on their roster that made an all nba team during their previous contract that was three seasons or more that team could have a salary of ~560M in theory.