Your vet is totally incorrect on this...........It will not heal and if you don't get it repaired very soon, arthritis will begin to set it. He will have a very unstable knee and get very severe arthritis from this injury.
My advice is to get him to a board certified orthopedic surgeon for an opinion on this.
Here is an informative link:
Yorkie Haven Rescue - Cranial Cruciate Ligament Tear Info