Sure can, but I really don't see a reason. Why would I like to fight against my own government and help some barbarians to retain their way of life? Depending on a character, an imperial doesn't necessarily care about the war and it's outcome, but to support stormcloaks.. Nah. Of course one can play some kind of freedom fighter, who supports rights of natives, but that sounds a bit odd to me.
Come to think of it, the conflict offers interesting opportunities. Can you choose to join both factions or change the side in the middle of the war?

Anyways, I like the imperial race, but I've never supported their cause in the war. Usually I just ignore the whole conflict. My stormcloak nord is an exception.

Never been one. Race wise or role-play wise. Don't care for the blokes, unless for beating the crap out of them.

Yea, that one had balls. Good thing he's not alive to see the Empire now.