I suspect not. The freelance market is fierce, and for a paper to be forced to bargain, a union would have to convince a widely-dispersed, unorganized group of individuals to join its cause. Currently, the National Writers Union (which is an affiliate of the United Auto Workers!) is only about 1,300 strong.
Let me explain:
Many papers, especially weeklies such as Isthmus, draw upon a large group of freelancers to produce regular articles. While it’s convenient for a paper to have a group of regular contributors whose work it can depend on, if the regular contributors demanded higher pay, the paper could probably function for a period of time with outside contributors, even if that meant a little extra work for editors or even lower quality. The damage would probably not equal that incurred by a factory if a large number of its workers walked out on the job.
As a result, the freelancers union advocates for its members differently than traditional unions. Whereas the chief goal for most unions is to bring collective bargaining to a workplace, the NWU is more of an advocacy organization that aids individual writers in understanding contracts, filing grievances against papers over backpay and providing health care options for freelancers.