tdol said:It would be very dificult to use your example. With action vebrs, the present perfect progressive is normally used to show that something began in the pas and is not complete. With the email examples, the speed of the action would generally indicate that it is finished. I culd say 'I've been sending him emails for several days and he hasn't replied'. Here, the action is incomplete because I wil send more emails until he replies. However, with 3 emails, you have basically sent them or not. ;-)
However, if you had many messages, you could say 'I have been sending emails all morning'.