Maybe. But for the up and coming indie rocker, or young New York theater company, probably not for much. Or at the very least, not for what it's monetarily worth.
In Merlin Mann's interview with John Vanderslice, an independent musician, John explained how one of the goals for his band's next album is to release it without any print advertising at all. This is partly on account of John being a hip-and-with-it creative person, but also because print advertising, relative to the internet, gives an inferior return on investment. And when your resources are limited, splurging tons of dollars on getting that newspaper ad just does not seem to make as much sense as doing a hot viral marketing ad on youtube, or even just putting up a myspace page.
The evolution of print marketing's relevance is very visible in the theater world. A short time ago, theater companies would print postcards w/ artwork and details of an upcoming show, and then mail them out to a list of subscribers to the companies' mailing lists. More recently, such postcards have made their best use as "lobby cards"-- filling in shelf space at rehearsal and performance places throughout the city. The actual postcard elements are minimized, and the majority of the space is taken up with show information, rather than leaving room for an addressee's address. The older model of sending targeted postcards seems less relevant for the young company with little money to spend. The "lobbycard" itself becomes nearly an anachronism in itself-- just a colorful piece of card you can hand to friends when they ask when your show is.
At a panel discussion among a handful of producers from the NYC area, the most useful anecdote was one by a producer who had done work at both carnegie hall, as well as small off-off broadway theaters. And one great distinction he realized was that, even with full page New York Times ads and print advertising, he got a better turn-out for the indie theater piece he was promoting through guerilla tactics, than he did with putting out print advertising among all sorts of wealthy folk for the Carnegie Hall event.
Does theater advertising need to go 100% web? Maybe not. Are postcards an anachronism of an older age? I'm mostly sure they are. Do upstart companies of any sort need to carefully assess their advertising dollars in the wake of free internet buzz and advertising? Most certainly.