Was Desmond telling the truth about Charlie's death leading to Claire's rescue?
Theory 1: Yes, Charlie's sacrifice was supposed to end up with Claire stepping onto a helicopter and being rescued
The Kahana did have a helicopter that she surely would have escaped on as Desmond described. She and Kate would have met in the forest where she, Jack and Sawyer met, and surely Claire, accompanied by Kate or Sawyer, would been a priority to get on to the helicopter or the boat.
This would have happened if Christian hadn't intervened. If Jacob can see the future (as the Others seem to rely on him to do), then Christian's intervention counteracted Desmond's and made sure that Aaron was taken off the island, Claire stayed, and maybe by extension that Kate would also be put in charge of Aaron for the day, and then for at least the next several years. This intervention has big consequences.
Desmond's interference in Charlie's inevitable death caused severe ripples in time changing things that were "meant to be". This is evidenced by Jack telling Kate that "they weren't supposed to leave the island", and by John Locke telling Jack that he "wasn't supposed to do this" after stabbing Naomi. The island began trying to kill Charlie after Jack brought him back to life due to Ethan hanging him.
In Desmond's flashes he never saw "Not Penny's boat" and by telling Claire about it she chose to stay with Locke instead of leaving with Jack.
Dominic Monaghan was meant to be in the show for the entire series, and leaving the show was his choice, so actually Charlie wasn't supposed to die.
Desmond saw separate things (the helicopter, everyone including Claire celebrating that they were going to be rescued, Jack/Kate/other O6 getting on the helicopter, etc), this is, separate images, and incorrectly concluded that Claire was going to be among the saved.
Kate came back to the Island to bring Claire off the Island, and to Aaron. Desmond DID see Claire getting into a Helicopter, just, not at the time Charlie thought she would.
Theory 2: No, Desmond had to get Charlie to complete the mission for other reasons and used the story of Claire to motivate him
At least once before (to retrieve Naomi and be back with Penny) Desmond risked Charlie's life. In the end, he was reunited with Penny and Charlie dies, and Claire wasn't rescued like he said.
Charlie was resigned to the idea that somehow his death was required for Claire's escape outcome to happen.
Charlie didn't necessarily have to die (meaning he could have survived and Claire still might be rescued), but his death was the result of a self-fulfilling prophecy. Desmond's visions are choppy flashes of the future, often in pieces and out of any context that he understands, and his assumption of a chain of events which needs to happen a certain way is incorrect. This means that the parachutist would have ended up being Naomi regardless of whether Desmond saved Charlie's life that day. However, because Charlie was working under this assumption and believed that he had to die in order to save Claire, he chose not to swim out of the room.
Desmond saw that he would be reunited with Penny and that Aaron would make it off the island as a result of Charlies sacrifice and tells him Claire will be rescued as well in order to sell this to Charlie. In "Catch-22" we see that Desmond could risk the life of a friend at the prospect of reuniting with Penny.
Theory 4: Yes, but Desmond misinterpreted his flash
He is talking about Aaron and Claire. Hurley left them when he switched from Ben and Locke's group to Jack's. Charlie wants his friend Hurley to help the 2 people he cares about most on the Island.
He wants Hurley to bring Aaron back to the Island.
He was merely a projection of Jacob, the same force that corralled the 815'ers together in the first place.
Hurley has been seeing visions of Charlie and says to Jack, "I think he wants us to go back." He is Jacob. Charlie is just a manifestation of Jacob, and Jacob appears as Charlie to provide a friendly/familiar face to Hurley, and to deliver him the message that "they need you". The message of "they need you" has been interpreted by Hurley as a message to go back to the island, as seen with his conversation with Jack while playing basketball. Jacob wants the Oceanic 6 back on the island so that they can fulfill their destiny as they were supposed to.
Jacob as Charlie could also explain why in "Through the Looking Glass, Part 1", Jack still thinks Christian is alive. Jacob has also appeared to Jack as Christian, in order to manipulate him back on the Island.
It really was Charlie, because when the bomb detonated in 1977 realities to split, causing one branch that actually had 815 land at LAX. My belief is that those that died on the island somehow retained the memories or the island. If both realities/memories somehow exist in the same timeline, Charlie would not flash back to the Island since he's dead there, but his conciousness would be free to move about this new reality like he landed. He would then go warn Hugo that he needs to return.
That was the impression we got in Series 6, but there was no reality split; the flash-sideways timeline was in fact the 'Afterlife', not an alternate reality.
Theory One: Jack Resuscitated Charlie
Jack is a doctor and has the medical knowledge to save someone in Charlie's position.
Theory Two: Charlie was the first person brought back to life by The Island
Charlie was dead for longer than a person can usually be and then be resuscitated. Jack even had a break from trying to save him and then went back to Charlie.