3.3 seconds asked this in the immediate reaction thread to Game 4 of the ECF. Out of curiosity, I decided to look into it a bit. Surprisingly, the answer is yes.
The year - 1962
The team - Los Angeles Lakers
The player - Elgin Baylor
Baylor's series started slow for someone who would average over 40 points per game. In game 1, he scored 35 as LA lost to Boston 122-108.
In game 2, he scored 36 as LA beat Boston 129-122.
In game 3, he hit 39 points (still under 40) as Los Angeles squeaked out a 117-115 victory.
Game 4 was a backslide, as Baylor scored 38 in a 115-103 loss.
Game 5 was where Baylor went off, scoring 61 points to take LA to a 3-2 series lead with a 126-121 victory.
Game 6 was a 34 point contribution in a 119-105 loss, and Game 7 saw Baylor drop 41 but LA lose 110-107, for a total of 284 points over 7 games, or 40.57 PPG, with LA losing the championship to Boston in 7 games.