I could almost certainly play my prot paladin on the majority of fights without paying much, if any attention to my resources and abilities. It helps that prot paladins have a pretty simple rotation and I could simply mash Shield of the Righteous constantly so that it goes off whenever the Holy Power is available. On fights where I actually have to use active mitigation properly, I could probably still manage as long as I pay attention to DBM timers.
As far as my warlock goes... I'd certainly see a DPS loss, but I could probably manage and remain relatively competitive. Resources fill at a relatively constant rate, so I'd probably lose an unbuffed/4pc buffed chaos bolt or three over the course of the fight, but I'd still be able to fire off my fully buffed bolts without issue (kind of hard to miss a big power aura :P).