To pick an arbitrary date in which most teams were at or around 20 games played, on April 27, 2016: the Chicago White Sox had an AL-leading 16-6 record and then proceeded to go 62-78 over the rest of the season and finish 4th in the AL Central. Looking at 20 games as a whole is problematic because each team has its own narrative of injuries, trades, losing streaks, winning streaks, cluster luck, etc. But at least we can get a snapshot of the importance of at least not starting off disastrously...like the 2016 Astros, who were 6-14 after 20 games.
Since 2012, when the 2nd Wild Card was introduced, 21 out of 25 AL teams (84%) that made the playoffs started the first 20 games at .500 or better. More to the point, in four of the last five years there has been one team to start the season with at least 13 wins in their first 20 games (2016 White Sox, 2015 Tigers, 2013 Ramgers and 2012 Rays) and managed to miss the playoffs.
2016: All five American League teams that made the playoffs were at or above .500 after 20 games. That doesn't necessarily translate to a big division lead - in fact, only one of the five AL playoff teams (Baltimore) was leading the division after 20 games. Texas, Toronto, and Cleveland were both 10-10. Boston was 11-9, and Baltimore was 12-8. Yet they all made the playoffs. The aforementioned White Sox went 14-6 and missed the playoffs.
2015: Three of the five AL teams that made the playoffs were at or above .500 after 20 games: Kansas City was 14-6, the Yankees were 12-8, and Houston was 13-7. Toronto was 9-11 after 20 games, and the Ramgers were 7-13. The Blue Jays and Rangers had the best and second-best records in the AL, respectively, from that point forward. Detroit was 14-6 and didn't make the playoffs. Boston and Tampa Bay were both 11-9 and met the same fate.
2014: All five playoff teams were at or above .500. Baltimore, Kansas City, and Anaheim were all 10-10. Detroit was 12-8 and Oakland was 13-7. The Rangers were 12-8 after 20 and didn't make the playoffs.
2013: Three out of five AL playoff teams were at or above .500 after 20 games. Boston, who went on to win the World Series, was 13-7. Oakland was 12-8 while Detroit was 10-10. Tampa Bay was 9-11 and Cleveland was 8-12. Texas was 13-7, went on to win 91 games and miss the Wild Card by one game.
2012: All five AL playoff teams were at or above .500 after 20 games. The Ramgers led the way at 15-5, followed by Baltimore (12-8), New York (11-9) with Detroit and Oakland sitting at 10-10. The Rays were 13-7 after 20 games and missed the playoffs by three games.
What does it mean for the 2017 Astros? Who knows? The Astros have played 11.7% of their season. Teams come out hot after 20 games and...then there's 142 games left to play. But while you don't win the division in April, you certainly can lose it in April.