Only peripherally. Churchill was born in 1874 during Victoria's
reign, but he would have been only 27 at the time of her death.
Churchill graduated from Sandhurst, the British Military Academy,
in 1894, and in 1896 went to Bombay, India. By 1899 he was back in
England, and ran for the House of Commons; he lost that election,
but was elected the following year, in 1900.
Queen Victoria died in 1901, so there would have been a one-year
overlap when Churchill would have been in Commons while Victoria
reigned. However, after the election Churchill embarked on a
speaking tour of the United States.