Henchmen have infinite energy and don't seem to suffer Death Penalty, but otherwise, they function pretty much as normal players. Same with enemies.
They take the same amount of time to use skills as players, and to recharge their skills. If you use Diversion on a warrior enemy (or hench, which is feasible during PvP in the tombs or against another guild), and they use Healing Signet, you won't see them using Healing Signet again for a while. If you use Blackout on them, they won't use any skills until it runs out.
That being the case, consider Resurrection Signet's recharge timer: non-existant. It never recharges... Except after a mission, and after you gain a morale boost (Saying defeat a boss would be redundant, as that = morale boost). However, since henchmen don't seem to be affected by DP, I doubt they gain Moral Boosts either, meaning no recharge. That may or may not be intended. The ability to ignore Death Penalty is very potent, but it is also said that they have that to deal with their incompetence. However, the same is said for their infinite energy.
I'd go with sending an e-mail to find out an official answer if it was an oversight or intended.