No not at all. They can absorb all the dead money this year or next year via the June 1st cut designation. Just because he would have been cut possibly in August doesn't mean the dead cap goes into next year. By default it goes in to the year the player is cut. You have to use the gimmick to move it to next year.
That's incorrect. The designation (or "gimmick") applies to transactions BEFORE June 2nd. You don't need to designate a person who is cut after June 1st as a post-June 1st cut. Because they are automatically that.
Explaining the June 1st Designation | Over the Cap
overthecap.com
"What we are talking about here deals strictly with the acceleration of prorated bonus money onto the current years salary cap. The NFL essentially breaks up its salary cap accounting for bonuses into two periods with June 1 being the trigger date. When a player is removed from a players roster prior to June 1st all his remaining unamortized bonus money immediately accelerates onto the salary cap. To illustrate this we see how the Kansas City Chiefs gave Steve Breaston a $5 million dollar signing bonus in 2011, which was accounted as $1 million in yearly expenses over the course of his 5 year contract. When he was released just the other day he had only completed 2 years of his 5 year contract meaning the Chiefs salary cap had only accounted for $2 million of the $5 million paid in 2011. The balance of $3 million dollars immediately accelerates onto the Chiefs 2013 salary cap.
After June 1 the NFL changes the way the acceleration works. After June 1st only the current years expense remains on the books after the player is released. The balance accelerates onto the following years salary cap. So in Breastons case had the Chiefs waited until June 1st to release him his salary cap charge in 2013 would have been $1 million and in 2014 he still would be on the books at $2 million dollars."