I don't think he's asking for if a Orc CAN be a dragonborn, more why would an Orc be dragonborn.
Because Orcs have been down-trodden by almost everyone else constantly, they may have no need to be a dragonborn and save the Empire/Stormcloaks. They don't care about the people in Skyrim.
But when Alduin ends the Kalpa, that is for the whole world. It'll end the Kalpa for the Orismer too, so logically an Orc would want to stop Alduin. The question may be why does he want to fight Dragons BEFORE he knows he is saving the world. It could just be for the challenge - he arrived in Skyrim as an 'experienced' warrior, and when he learns he can fight dragons he does it for the new experiences, then realises he must save the world?
Or he could be an Orc raised in the Imperial City, fleeing the damaged province of Cyrodiil and looking for a new home. If he was treated well in the Impreial City he wouldn't care (as much at least) that the Orismer are badly treated else where.