They can get into the postseason, but they'd have no shot. None. Pitching wins in the postseason. It's a big reason they got their last 4 titles. When they've had lesser rotations, they haven't made a dent in the postseason.
The only team to win the World Series in the past 30 years without an ace was the Kansas City Royals in 2015 (3rd ranked pen in '15, 1st ranked defense).