No. A fair catch is defined as a receiving player waving one arm in the air before catching the punt. This means that the play will end once the catch is made; the punt returner's team will get the ball at the spot of the catch and no return attempt can be made.
Currently, the NFL player with the highest punt return average is Michael Spurlock for the Tampa Bay Buccaneers, with a 30 yard average. He only has three returns for a total of 90 yards, however, he made fair catches on many more punts than that.
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