There is great information in the existing answers, but I believe the answer to the question is "No" Tolkien did not confirm this interpretation of **why** Galadriel gave Gimli three hairs. 

The story of Fëanor asking three times for some of Galadriel's hair is in *The Peoples of Middle-earth.

>For Fëanor beheld the hair of Galadriel with wonder and delight. He begged three times for a tress, but Galadriel would not give him even one hair.

>><sub>*The History of Middle-earth* Volume XII, Part Two, Chapter XI: *The Shibboleth of Fëanor*</sub>
><br><sub>Page 337 (Harper Collins 2015 paperback edition)</sub>

As Buzz points out in a comment, this was probably first written after *The Lord of the Rings*. The version I quoted was, according to Christopher Tolkien, written in 1968 or later. 

Might Tolkien have dreamed up the story later to give additional meaning to Galadriel's gift to Gimli? Perhaps; or perhaps the he already had already formed the story of Fëanor's request an it influenced what he wrote about Galadriel and Gimli. 

In the end, I think we have to accept the story of Fëanor asking three times for a tress of Galdriel's hair as canon. In that case, Galadriel giving Gimli three strands of hair when asked for one was either a coincidence or not. I choose to believe it was not, but you can choose as you like (and I think Tolkien would like that).