It seems that the crack might not be too large that's why doctors are thinking of giving a temporary crown. This way the want to see the healing time of the tooth. If the pain and sensitivity subsides after placement of a temporary crown then there will be no need for an RCT but if the pain continues then RCT will be advised.
Regarding having RCT without crown, it is generally advisable to get a crown after RCT as the RCT tooth becomes brittle and can't bear the masticatory forces. For more info on RCT visit the link....http://www.identalhub.com/article_why-is-root-canal-treatment-rct-required-299.aspx