TBH I'm actually really, really, really curious.
See, we go both ways on the Olympics as a community.   There seem to be about equal portions of people that hate them and that love them.   There's an immense depth of conversations on the site about the issue, and lots of content regarding the athletes that will be competing.
As one of the newest (and I'd bet anything hottest) sports in the Olympics, I'd imagine that there is going to be some attention that comes our way.
We're certainly bracing for a traffic impact.   Paul has actually been working hard for a few years now to really beef up the code for speed so it can handle the potential traffic spikes around Olympics time.  We don't know if that will be 20,000 extra people or 2,000,000.   Its so hard to say how things are going to react.
My gut says that we get a massive influx of lurkers around Olympics time, simply from the raw quantity of international google searches trying to learn more about this new 'freeskiing' stuff.  (said from the perspective of an average armchair olympian).  I'm sure we'll convert a few members, but I don't think it will be anything ludicrously substantial.
I do think that due to drastically higher mainstream attention, more Parents will be considering this vein of skiing to be something they can 'send their kids into' at an early age.   Thusly, its only a matter of time before those people discover Newschoolers, so we may see an increased long-term flow of members.
TL;DR:  Massive spike during, slow and slightly higher growth for years after.