Does Lieutenant Colonel John Sheppard get promoted to general in Stargate?

ANSWER 1

Until the final episode of season five, John Sheppard has not been promoted to General, yet. Thus, we still have to wait for the up coming seasons for Stargate Atlantis since it has not ended.
ANSWER 2

He might in the movies! (Hope he does!)
ANSWER 3
If he was still a the same rank as in season 2, he would be promoted to "full bird" colonel, not general.