No, but I think he would join the majority in order to be the one to write the opinion. When in the majority, the Chief Justice decides who writes the opinion.
If five justices are aligned against him on the wording of a majority opinion I would think they would have the power to relegate the Chief Justice to the second-best option of submitting a concurring opinion all on his own. That is to say, Riberts would seem not to have the unilateral power he might wish to have to water down an opinion held in common by five of his colleagues, however pure his mitives might be on that score.