Was Bran's accident a precondition for his recruitment?

Question

I wonder if Bran would have had the same fate without having his accident.

Bran started to dream about the Three-eyed Crow whilst he was in a coma. It appeared then that

the old Three-eyed Crow is recruiting his own successor and he chose Bran.

I don't know if the former Three-eyed Crow, Brynden, was himself injured and how he was recruited.

Do we know if being crippled is a condition to do the "job"? Being in a coma, was it a condition to be reached, through the dreams?

Answer 1

Nobody knows the answer to this question yet. But as GRRM says, everything shall be explained in due time. So this will be mere speculation based on canon evidence.

Who is Three-eyed Crow?

The Three-eyed Crow is beyond a doubt Brynden Rivers, son of King Aegon IV and known as Bloodraven.

The last greenseer, the singers called him, but in Bran's dreams he was still a three-eyed crow. When Meera Reed had asked him his true name, he made a ghastly sound that might have been a chuckle. "I wore many names when I was quick, but even I once had a mother, and the name she gave me at her breast was Brynden."
_{ADWD-Bran III}

Also:

"But," said Bran, "he heard me."

"He heard a whisper on the wind, a rustling amongst the leaves. You cannot speak to him, try as you might. I know. I have my own ghosts, Bran. A brother that I loved, a brother that I hated, a woman I desired. Through the trees, I see them still, but no word of mine has ever reached them. The past remains the past. We can learn from it, but we cannot change it."
_{ADWD-Bran III}

This fits because:

• Bloodraven loved either Daemon or Daeron II, both his half brothers.
• Blooraven hated Aegor Rivers, his half brother.
• Bloodraven was infatuated with his half sister, Shiera Seastar. She was one of the chief reasons of the rivalry between Bloodraven and Bittersteel.

Also we have his physical appearence where Bran observes that he bears the birthmark Bloodraven had:

What skin the corpse lord showed was white, save for a bloody blotch that crept up his neck onto his cheek. His white hair was fine and thin as root hair and long enough to brush against the earthen floor. Roots coiled around his legs like wooden serpents
_{ADWD-Bran II}

He also confessed that he was a brother of the Night's Watch in the same chapter:

"Are you the three-eyed crow?" Bran heard himself say. A three-eyed crow should have three eyes. He has only one, and that one red. Bran could feel the eye staring at him, shining like a pool of blood in the torchlight. Where his other eye should have been, a thin white root grew from an empty socket, down his cheek, and into his neck.

"A … crow?" The pale lord's voice was dry. His lips moved slowly, as if they had forgotten how to form words. "Once, aye. Black of garb and black of blood."

Did Bloodraven himself had any near-fatal experiences?

We know that Bloodraven must have faced two near-death events:

1. He suffered a greivous injury to his head/face in duel against his half-brother Aegor Rivers aka Bittersteel. He lost his eye as a result but survived.

   He stared so hard that Bloodraven felt it. The king's sorcerer had turned to study him as he went by. He had one eye, and that one red. The other was an empty socket, the gift Bittersteel had given him upon the Redgrass Field.
   _{Dunk & Egg: The Sworn Sword}

2. He was lost beyond the wall so it is possible that he may have faced a near-death experience out there due to exposure if nothing else.

   Bloodraven would rise to become Lord Commander of the Night's Watch in 239 AC, serving until his disappearance during a ranging beyond the Wall in 252 AC.
   _{TWOIAF: Aegon V}

Did Jojen and Bran face any near-death experiences before being chosen?

We have example of Jojen as well. Three-eyed Crow came to him when he was almost fatally ill. He came to Bran when he was also near-death.

Summer raised his head from Bran's lap, and gazed at the mudman with his dark golden eyes.

"When I was little I almost died of greywater fever. That was when the crow came to me."

"He came to me after I fell," Bran blurted. "I was asleep for a long time. He said I had to fly or die, and I woke up, only I was broken and I couldn't fly after all."
_{ACOK-Bran IV}

Conclusion

If we observe the pattern here, two things are common:

1. All three were followers of the old Gods.
2. All three were in a life-threatening situation.

So by that logic we can infer that yes Bran's accident was necessary for his recruitment.