Not any more than it's possible to get a virus from any other site on the internet. Which is to say, almost impossible.
I guess there's a small chance that an advert may lead to a less reputable site but that has never happened before and I've never heard of it happening on any other site. Or if someone posts a link in an answer to a bad site. But then that's a different site giving you the virus and not this site.
In short: NO.