Let me be the one who says NO. It is a bit hard to handle an infinite number of monkeys (because you will need an infinite number of bananas to feed them), but if you agree to have a finite number of monkeys and infinite time, I would guess that considering the time it should take for this to happen, it is likely that the universe would die before it actually does.
To quote a chat of one of my friends with my first year "intro to CS" professor:
professorProfessor: "So there is no chance that a fair coin would fall with the head side up 50$50$ times in a row."
myMy friend: "No!, there is such a chance it's just very small...."
professorProfessor: "Well yes, itsit's like the chance for all the nitrogen molecules in the air to gather around your head and have you die from lack of oxygen."