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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.

The three-eyed Raven 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 (Daeron II or Daemon), a brother that I hated (Aegor), a woman I desired(Shiera Seastar). 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}

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}

We have example of Jojen as well. Three eyed raven 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}

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.