The long and the short of it is no, she does not. In fact, even divorce does not entirely undermine marriage as much as same-sex marriage, at least it doesn't as it is currently considered, although it could if some of the more radical people get their way.
As horrific as Britney's 55-hour marriage to Jason Allen Alexander (not to be confused with Jason Alexander of Seinfeld fame), the fact of the matter is that it does little to hurt traditional marriage for most people because no one takes it seriously. What she did is a joke. People who get hitched and unhitched over the course of days or weeks are generally considered to be punchlines that everyone looks down on. There is little or no movement for the U.S. to make one-day long or one-week long marriages socially acceptable.
Even divorce is not looked at as a good thing, generally, but as a necessary evil. Very few people think of divorce as the natural end of a marriage. Almost everyone thinks of divorce as meaning that a marriage "failed," regardless of what folks like Kerry Howley and Meghan O'Rourke think.
The idea that marriage is by its nature only a temporary union and that divorce, rather than a way to end a relationship gone wrong, is simply the termination of such a union, could very well be seen as more disruptive than same-sex marriage, because it likewise degrades the traditional definition of what marriage is.
But the point is that no one sees it this way.
On the other hand, same-sex marriage is not out there to be seen as some sort of sop to those who cannot succeed as heterosexuals. It is not merely a concession to their weakness and inability. Rather, it is being set up as normal, natural, and as no better or worse than opposite-sex marriage (or, as I like to call it, "marriage."
The only way to make same-sex relationships equal to marriage is to degrade marriage to the same level as same-sex relationships. This is, by the way, why feminists who hate marriage are so gung-ho for same-sex marriage. The fact of the matter is, it isn't enough for the feminists and gay advocates, etc. to have their rights, they must tear down anything and everything that cannot easily be converted to become relevant to their lives.
That is all.