Prepare yourself with the new Game Guide!

Your installation of StarCraft II: Wings of Liberty has completed. Your fingers are itching to get into the war. But ask yourself this, marine: ARE YOU PREPARED?
Your adventures might take you to the far reaches of the Koprulu sector. Would you survive on New Folsom? Can you find your way from the fringe world Shiloh to the backwater planet of Mar Sara?
How much do you know about those you are about to face? Like Kerrigan with her bloodcurdling zerg Swarm? Or Zeratul and the mighty protoss army? Or even your own allies: how many of them can you trust? What do you know of their backgrounds or how they became who they are?
Don't get rattled just yet, recruit - we have something helpful for you here. Take the opportunity to check out this new Game Guide. There you’ll find an interactive Koprulu sector map; the cast of StarCraft II characters, including biographies and animated portraits for everyone you need to know; and of course a full description of each and every unit, including comparisons and previews.
Are you still here? Hurry up! Time's ticking away!

Or, according to this source, http://www.teamliquid.net/forum/viewmessage.php?topic_id=139767, in about 18 months.
SCII is a single-player trilogy, where each race getting their own game to complete the story. Answer to your question is no. You will only be able to plays as terran for now.