No.
The Stingray works by getting the phone to report in to what it thinks is a cell tower. That's what phones do when they are on but in standby mode, but not when they are off. That's why you can walk off a plane in a strange city and suddenly receive a call. When you turned your phone on, it checked into the nearest tower, updating the carrier's database to show your phone now in the new city.
BTW, that standby activity is also why battery life depends on how far you are from the nearest tower. If you are far from a tower, the phone needs to transmit at higher power in order to check in, draining the battery more quickly. My phone's battery will last a week in standby if I can see a tower out the window, but only a day or two if I'm in a fringe or no-service area.