That really depends on the rescue dogs' condition.
Generally their condition is decent. Good shelters tend to only re-home dogs that score well in sociability and training.
A rescue dog — unless maybe really, really old — needs to be challenged constantly. And by challenged, I mean — these dogs are/were rescue dogs for a reason. :)
Challenges include games and tasks, and all that. These dogs need "work" to feel alive.
Your talking about police/fire/ems dogs, but they are talking about saved dogs from bad situations.