Yes, sometimes a rookie pitcher will win 20 games.
Since the beginning of the expansion era (1961), only one pitcher with rookie status has won 20+ games -- Cincinnati's Tom Browning, who went 20-9 in 1985. Browning had pitched 23.1 innings in 1984 (and had a perfect game in 1988).
The last pitcher to win 20+ in his first major league season was the Yankees' Bob Grim in 1954, when he posted a 20-6 mark (and never came close to repeating that).