Establishing the scope of the negotiation (ie. what does each side care about?) is what inexperienced negotiators typically miss.
Smart legislators understand this, and use time to defeat opponents. That's why you see so many 11th hour deals.
Now once you've got the basics and want to understand more fully the how and why of swimming/negotiating then learning fluid dynamics/game theory may provide some insight but I very much doubt that knowledge of either is really going to give you much edge over someone who concentrates on learning the practice itself.
But then you get an insight and create these: http://en.wikipedia.org/wiki/Swimfin - and win without much effort.
It of course wouldn't help you much in a swimming contest, where the priority is for the whole game to look 'fair' to viewers, not to Just Win. But in real life, you're not always artificially limited by a set of rules that disallow using advanced knowledge for your advantage.