The answer is yes but you can't practically observe it. The electrons repel each other so strongly that you can't accumulate enough of them in one place to be able to observe change of mass of that object.
You can move whole charged atoms, that's a form of electricity too, and it can add observable amount of mass, like with electroplating or welding. But these very quickly turn electrically neutral after depositing.
You can move whole charged atoms, that's a form of electricity too, and it can add observable amount of mass, like with electroplating or welding. But these very quickly turn electrically neutral after depositing.