the team that finished in 06-07 is definitely worse than a healthy 13-14 squad. That said, if Rondo and Sully are held out, then unhealthy 06-07 is probably better than unhealthy 13-14.
everybody LOVED big Al in 06-07. he was touted as the next big thing. Why else were so many people broken up about trading him for KG back then? for comparisons sake, Jeff Green is nice but he wouldn't have been able to net us a 31-year old Paul Pierce.
and to answer the OP, i think the 06-07 squad - given time to develop - would have been competitive (i don't know if 'contender status'), although its success would have also been quite reliant on Ainge drafting another good player with his picks in those 2-4 years of mediocrity.
As an interesting sidenote, I don't think Rondo would have developed as quickly if he had not been part of the KG-culture Celtics.