I doubt there will be any crowds on the slopes.
Russia doesn't have a lot of skiers, and those who do ski usually have the time and money to go to the Alps. Russia also doesn't have a lot of foreign tourists because of the visa requirements, lack of cheap flights, and language barrier.
It's expensive and time-consuming to get to Sochi from anywhere outside of Russia. On top of that, it's near the most dangerous parts of the country, with Dagestan, Chechnya, and other regions in the immediate neighborhood. So, very few people are willing to go there to ski (Russians only go there in the summer for the beaches).
I'm sure the Olympics will increase the numbers on the slopes, but it will be an increase from an extremely small number to a not-quite-as-small number. So, the potential crowds really wouldn't be a factor for me if I were in your shoes.
However, there are plenty of other things worth thinking about. Are you willing to spend that much time and money to go to Sochi when you could get to the Alps more easily from just about every part of the world? Would the increased security threats in an already dangerous area make you feel uncomfortable? Are you willing to take your chances with Russian service given how poor it is compared to other parts of the world (I've lived in Russia, so I can attest to that)? Are you willing to spend your vacation in an area where your main method of communication would probably be pointing and gesturing (assuming you don't speak Russian)?
If you are ok with all that, then I'd say you should go for it.
Edited by CerebralVortex - 9/8/11 at 5:51am