The odds you posted are based on the assumption every game is an even match. In other words, when picking a North Carolina over an Oakland in the first round, it wouldn't be fair to suggest both sides have an even chance to win the game. Your odds would be more on the lines of, "yes thats right 19 quintillion to one....to pick the correct pointspread winner of every game."
While in theory, each of the 63 games offers a 50/50 chance, reality suggests that many of the early-round games are GENERALLY (bucknell, Wis-Milw prove nothing is a lock) easy picks.
That being said, I think it's safe to say none of us will EVER!! pick a perfect bracket. Whatever the odds, they are just too remote.
By the way, how'd you know 18 zero's was the equivalent to a quintillion??