Based on my experience with VANOC well in advance of the Winter Olympics here in Vancouver - NO. I was in the process of making Olympic Anagram T-shirts (Olympian = Palimony) etc. and they threatened to destroy my life if any of my ART was found being sold online, on the street or on Mars. True.
Also, given that the Olympics have become a political battering ram to push through, at all levels of government, any project at any cost at any consequence in the future, the answer is still - NO.
As a Canadian, living in Canada, a country with NO "fair use" provisions because our laws are derived from those of the United Kingdom, I am well aware of how copyright and trademarks work. The Olympics are a rarefied, global, multinational corporation that demand governments bend to their will with respect to their trademarks if they want the games. Governments do so because it brings in revenue and also allows them to undertake mega projects that would otherwise never see the light of day.
Also: For the 2010 FIFA World Cup the airline Kulula called itself the "Unofficial National Carrier of the You-Know-What". The ad was pulled when a complaint was lodged, though.
Careful where you say that... they might brand that, too.