Not in the first release of the game, it appears. The official games may not be ready to unleash Orc-players, but at least one unofficial gaming group has taken the plunge. These Orcs seem a little better educated and talkative than Tolkien's Orcs. Somehow, I don't think Sauron would have funded an Orc Academy for the Fine Arts. Education has traditionally been portrayed as a threat to tyranny.
Ignorant masses are easier to manipulate than educated masses.
Online gamers have probably long since heard about Elendor MUSH , a Multi-User Shared Hallucination founded in 1991. There are many Web sites out there devoted to the MUSH, but not many which celebrate the Orcness of Being. Playing an Orc in a movie should be relatively easy compared to playing one in an ongoing game. In a role-playing game, the Orcs should be as motivated to survive as the Elves, Dwarves, and Men. And they probably get bored just like everyone else too.