If the new labor deal is really to be ratified on July 21, then that should work for the Green Bay Packers. They'll be rushed to sign their free agents and draft choices, but so will every other team. And I'd expect the Packers will have nearly all their players signed and ready to report on time, so a few stragglers won't set the team behind. Having the continuity of the same coaches, and almost every starter returning, will help them transition back into camp.
Much of the same holds true for the Chicago Bears. They have some issues to work out on offense, but they're returning with the same offensive coordinator and scheme. Their defense, with veterans like Brian Urlacher and Lance Briggs, can probably run the defense in their sleep. While it looks very likely that they'll start training camp late, and probably have to cancel their first preseason game, it shouldn't put them far behind.
That Hall of Fame preseason game on August 7th is always very early, and is usually played as the Packers are just finishing their first week of training camp. The coaches might disagree, but the players probably won't miss that first preseason game. I'm not sure even rookies will miss the opportunity to play because their performance in the later preseason games is usually what makes or breaks them.