No, this is an internet myth, and it's not very logical. During the last war when there was a draft-- Vietnam-- in the 1960s, Barack Obama was a young child (he was born in 1961). By the time he was in his teens and old enough to join the military, the Vietnam War had been over for a while. There were no other wars at that time, and there was no draft either, since the US had gone to an all-volunteer force. Barack Obama went to college, and did not "dodge" anything.