Tolkien did not confirm this (plausible) interpretation
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 Unfinished Tales and 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.
Unfinished Tales Part Two, Chapter IV: The History of Galadriel and Celeborn
Page 230 (Houghton Mifflin 1980 hardback edition)
Also The History of Middle-earth Volume XII, Part Two, Chapter XI: The Shibboleth of Fëanor
Page 337 (Harper Collins 2015 paperback edition)
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 (in both Unfinished Tales and The History of Middle-earth), written in 1968 or later.
Might Tolkien have dreamed up the story of Fëanor's request after writing The Lord of the Rings in order to give additional meaning to Galadriel's gift to Gimli? Perhaps; or perhaps the he had thought of the story earlier and it influenced what he wrote about Galadriel and Gimli in The Lord of the Rings.
In the end, I think we must accept the story of Fëanor asking three times for a tress of Galdriel's hair as canon, and that in-universe it happened before Gimli met Galadriel. 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 be okay with that).