Woody Allen uses the term as well, in a context implying
that it's an old, old term, and not specifically gay.
In that film, Allen is a "beard" when he is the escort for
a mobster's mistress (thus allowing the mistress to have an reason for being at a place where the mobster will be, without appearing to be there with the mobster).
The practice is ancient; it was an old idea in Elizabethan
times, when kings would have their mistresses marry a presentable non-entity. The "husband" would be rewarded with lands, but it was strictly hands-off (until the king tired of her...). See the film "Restoration" for a plot based on this practice.
-John