Yes 

A fathom equals six feet.

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Editor: Michael, your point is well taken. But the MooT question is:

Now, as one of the Concise Oxford's definitions of the word is "a measure of 6 feet," the only possible answer to the question is "Yes" -- a person CAN grow to be a fathom in length -- and there is nothing anachronistic about the use of the word fathom in this context. Thanks for your interest.