Here is the USBC rule on bowling out. Unless the league rule specifically says that he can't I see no reason why he shouldn't be allowed to.
106d. Bowling Out
Unless the league rules state otherwise:
1. Adult leagues: A bowler may finish any one game of a series before teammates or opponents.
2. Youth leagues: A league member may not finish any game of a series before his/her teammates or opponents, unless the league official/supervisor determines an emergency or sufficient cause exists.
Scores recorded while bowling out count in deciding the game and bowler’s average, and qualify for USBC awards and league awards.
NOTE: A player bowling out should do so while the others continue to bowl. The player should bowl on each lane immediately after the previous bowler completes the frame, so that the progress of the game is not delayed.
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Jason K

But be not afraid of greatness: some are born great, some achieve greatness, and some have greatness thrust upon them.-W. Shakespear
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