No, because the mix ratio in both glasses has remained the same.
Because there is the same amount of liquid at the end of the experiment, as much lemonade must have been taken out of the tumbler as there is beer remaining in the tumbler. It makes no difference whether it was stirred or not.
Try it with the following example: assume that the liquid in the second tablespoon contains 90% lemonade. You add this to the beer. There is 90% (one tablespoon) of beer missing from the beer glass. This amount has remained in the lemonade. It can be concluded that only an exchange of liquid has taken place, because there is the same amount of liquid in both glasses again.