While this makes sense technically, this has not been my experience. My office is less than 10 feet from my Model 3 all day and my car successfully sleeps hours on end. Here's my last 6 days. Green is asleep. Most of the time, it will sleep ~24 hours and them come out for 20 minutes to check in with the mother ship.
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I even went to the car and stood next to the drivers mirror (where I believe the BT antenna is) and the car was never awoken. I walked around the car less than a foot away with my phone out and display on and the car never awoke. I had to slight press the door handle (a trick I use when plugging/unplugging the wall charger) to get it to wake up (but not unlock). Only when I did that did the car wake.
My guess based on this admittedly limited data is having your phone close to the car does not wake the car.