Docs can you explain, is root canal treatment possible for half broken molar due to caries?

Usually: Many badly broken down teeth can be saved through a root canal (endodontic) procedure and a core/crown. Some teeth, however may be so structurally compromised that a good result is unlikely. You should see your dentist or endodontist to determine what is right for you. More info can be found at: http://www.Aae.Org (look under the "patients" section.

Yes: If the tooth does not have any other fracture and good to restore, then yes that's what is normally done in cases like this..

Root Canal: If it is determined that by the dentist that the fracture and decay are not too extensive that the tooth cannot be restored, then by all means root canal away, and you won't lose the tooth in most cases that way. ;).