My opinion is that jumping citizenship would be a blatant attempt to subvert the rules, and I'd hope that a threat of a rule 69 action might discourage it.
Well, let me soften that a little. It would be much simpler to say that everybody on board must have been citizens since a day before the previous America's Cup was held. If a sailor possesses dual (or multiple) citizenship, he must have declared a primary affiliation for that same period. That wouldn't require any threats.
Frankly though, I don't want someone becoming a citizen of the USA (with the intent of switching allegiance again afterward) for the sole purpose of sailing in a regatta. If you don't intend to keep the vow given to gain citizenship, don't give it. Naturalization under false pretence shouldn't be just unsportsmanlike; it should be illegal.