Yes. The demonstration of this fact is actually a famous anecdote in the history of statistics. Ronald A. Fisher, one of the towering figures in the history of statistics, gave the case as an example in the second chapter of his book The Design of Experiments (1951), without mentioning it being based on a true story. Some references can be found on the Wikipedia page for Lady tasting tea. A detailed description of the experiment can be found here, where one can find the following account from R. A. Fisher: The Life of a Scientist (1978) by Box:
Already, quite soon after he had come to Rothamstead, his presence had
transformed one commonplace tea time to an historic event. It happened
one afternoon when he drew a cup of tea from the urn and offered it to
the lady beside him, Dr. B. Muriel Bristol, an algologist. She
declined it, stating that she preferred a cup into which the milk had
been poured first. “Nonsense,” returned Fisher, smiling, “Surely it
makes no difference.” But she maintained, with emphasis, that of
course it did. From just behind, a voice suggested, “Let’s test her.”
It was William Roach who was not long afterward to marry Miss Bristol.
Immediately, they embarked on the preliminaries of the experiment,
Roach assisting with the cups and exulting that Miss Bristol divined
correctly more than enough of those cups into which tea had been
poured first to prove her case.