I generally find the e-prescribed meds arrive rather quickly at large retail chains. On more than one occasion, I've sent an e-script only to have the pharmacy call the patient's cell phone while I'm still in the room with them.
That happened to me for the first time the other day. I was wrapping up the visit and the patient got a call or text from the pharmacy and said they had a refill. I asked, "You need a refill on something else?" And they said, "No, the pharmacy just got the one you sent!"