The answer's no. Director Phillips stirred up a firestorm of controversy when he gave an interview prior to the film's release claiming the monkey (a 17 year old capuchin named Crystal) was taught how to smoke and is now addicted to tobacco. It was a joke, but it didn't translate well in print. In reality, the smoking scenes were actually pulled off using CGI. The smoke and the burning end of the cigarette were created by visual effects supervisor Robert Sttadd.
Todd Gunderson, Crystal's trainer, says Crystal actually hates any form of smoke. "Ethically speaking, neither I nor Todd—who loves animals—would have ever let her hold, let alone smoke, a lit cigarette, even if it weren't against AHA regulations, which it is," stated Gunderson. "But there was never even a question."