The short answer to this question is… maybe. Picking all of the favorites in the first round definitely maximizes your chances of getting as many first round picks correct as possible. But depending on how all of the potential matchups break down in subsequent rounds, it may not be optimal (in the sense of maximizing your chances of a perfect bracket.)
To see why, let’s consider a simplified example of four teams. Say those teams are Syracuse, Robert Morris, George Washington, and Gonzaga (the top left quadrant in Jerry Palm’s projected bracket as of Monday). For simplicity, let’s just assume that Syracuse beats Robert Morris. Then the question becomes, which is most likely to happen: 1) GW beats Gonzaga and then Syracuse beats GW or 2) Gonzaga beats GW and then Syracuse beats Gonzaga. (Presumably Syracuse winning in the 2nd round is more likely than an upset by either of the other teams, so we can eliminate those possibilities too.)
Syracuse would be favored against either Gonzaga or GW, but let’s just assume that Gonzaga matches up much better against Syracuse than GW does, so Syracuse would have a 70% chance of beating GW, but only a 60% chance of beating Gonzaga. Let’s also assume that Gonzaga also has a 53% chance of beating GW.
If I were to pick favorites throughout the bracket, I would pick Gonzaga over GW and then Syracuse over Gonzaga. That outcome would have a 31.8% chance of playing out (53% * 60%). On the other hand, GW beating Gonzaga and then getting beat by Syracuse has a 32.9% chance of occurring (47% * 70%). Thus, the most likely complete sub-bracket here involves Gonzaga being upset (albeit slightly).
How realistic is this scenario? These sorts of things can happen, especially when other circumstances come into play (say hypothetically the second game here were going to be played in Spokane, giving Gonzaga a huge relative advantage over GW). Nonetheless, they don’t tend to be major factors, so generally picking the favorites to win in each round as you fill out your bracket will be near optimal in terms of maximizing your expected number of correct picks in a bracket game (note: not necessarily optimal in terms of maximizing your expected score, but we will get into that later), as well as maximizing your chances of that elusive “perfect bracket.”
It may not maximize your chances of actually winning a billion dollars though, because odds are, you won’t be the only person following this strategy. So in the off off off chance all 63 of your picks come in, you will actually have to split the money.