Ron Weasley was believed to have used Felix Felicis during the Gryffindor vs. Slytherin match during Half-Blood Prince, if not by the school authorities then at least by Ron and Hermione. Ron's flying was unnaturally good.
With half an hour of the game gone, Gryffindor were leading sixty points to zero, Ron having made some truly spectacular saves, some by the very tips of his gloves, and Ginny having scored four of Gryffindor's six goals. This effectively stopped Zacharias wondering loudly whether the two Weasleys were only there because Harry liked them...
(Half-Blood Prince, Chapter 14, Felix Felicis).
It eventually emerges that Ron didn't take Felix Felicis at all but was operating under the effects of placebo. Nevertheless, he convinced Hermione and his performance may have raised doubts amongst the teachers for being especially strong. Yet Ron is never reprimanded or questioned for using a banned substance, even when the teachers knew that Ron's close friend had a batch of Felix at his disposal.
This may be because allegations of doping are difficult (or impossible) to prove, or because Hogwarts-level Quidditch is too small-fry to conduct such investigations. We don't know either way.
Presumably players competing in the British and Irish Quidditch League or the Quidditch World Cup would be subject to greater scrutiny. There would be little point in making Felix Felicis a banned substance if the rules were not enforced. There's no detail in canon of any anti-doping operation, however - even in the companion book Quidditch Through the Ages - so this point is pure conjecture.