I'm going to cut against the grain here and say yes, a lighter bike will help. Could you do the tour on your current bike? Sure. But since you are traveling that far for that long, even a small decrease in weight will help over the long haul. Will it help you get 3mph faster? Probably not. Your training will help you get faster.

A lighter bike will make the tour easier on you, as long as it's not a significant burden on your wallet.

Just my $.02