I would echo what both Robert and Alex said, but just from the official NATO standpoint in their 2010 strategic concept, the last one that was created, it was mentioned explicitly that, as long as nuclear weapons exist, NATO shall be a nuclear alliance. They have continued to mention that.
Of course, since it is a consensus organization, there's always a lot of opportunity for discussion, but as they have already created consensus on that issue, I think it would be rather challenging to get around it at this point.