At least, not yet.
As an academic, I am very much in favor of open access. It provides honed arguments upon which academics can build new work. It allows for research to become publicly visible, and quickly. Most are refereed journals, with some degree of clout. Advances in Historical Studies, published through SCIRP (Scientific Research Publishing), provides a place for scientists and historians to discuss new discoveries and methodologies in the historical field. As an open access journal, the cost of publication is the responsibility of the author, and not absorbed by the corporation.
There are two major problems right now:
1. Open access has an online focus. This means that the papers are available primarily online, though some publishers produce print copies, like SCIRP does. The problem with this is the longevity of the work. Online data deteriorates, and companies dissolve. When these things happen, where does the academic work go? Are the papers in open access journals housed in any physical way?
2. The second problem is more social. Internet access is not yet a right, or a reality for all people. Those who need to access academic but do not have access to the internet cannot rely on open access journals that do not exist in an analog world.
These problems can be solved relatively simply, as SCIRP does: a small run of each issue in print can (and should) exist in a few locations, available for purchase by request. Public access still exists online, but they become more permanent in print. Thus, the information perpetuates, and the journal maintains its relevance.
An additional problem, already somewhat addressed in print journals, is the obscurity of some topics. For example, the wonderfully-titled Biannual Online-Journal of Springsteen Studies, or BOSS. Very specific, peer-reviewed, academically relevant, but extraordinarily specific. Where do works like this fit into the larger academic picture?