John would have to comment, but my suspicion is that most of the measurements it displays are based on the barometer, not the accelerometer (only the G figures come from the accelerometer I think, and maybe some timing like the burn-out time, but not velocity info, etc). If you turn on display of the accelerometer data or email yourself the Excel file you might see something more, though assuming it's exposed to the air after separation I'd think you'd at least be okay from that point on, not sure if it gets confused by not seeing a 'proper' baro ascent however. I guess it might even see ejection as the start of the flight, then see the pressure increase and assume it's already landed. Try your 'chucked it up into the air' trick in a rigid sealed container and I suspect you may not get any data at all (can't think of a good way to break the container seal at 'apogee' to simulate that).
But I'm particularly confused by 'I'm out of range by the time I drop off my flight card'. At least all the launches I've ever been to that's done at the RSO(/LCO) desk, then you go prep your rocket on the pad, then they fly it. I think you really want to be arming the AltimeterThree after the rocket is situated on the rod/rail (I always load the rocket, arm all altimeters, whether just logging or for deployment, then install the ignitor). If you move it too much after the altimeter is armed it could get confused and think it already flew, missing the real launch event later (I had this happen to me once with the A3).
So for me it's always: Attach A3 to rocket, power it up, seal up the rocket. Hand flight card to RSO and head out to pad, load rocket on pad, connect to A3 and set to Record mode, load ignitor, walk away. I'm becoming increasingly convinced that it's important to quit the A3 app before walking out of range (i.e. hit the home button), I've had several instances of difficulty re-connecting upon recovery, all where just power-cycling the A3 lets it re-connect (no amount of power-cycling the phone, force-quitting the app or trying to manually disconnect/re-connect the BT connection helps), but sometimes the flight data is gone at that point (downloads nothing or downloads something like you describe, many seconds with a max altitude of a few feet), other times a proper download happens after the A3 power-cycle and all is good. But the difficulty I have connecting (iPhone 6s, everything up-to-date) sounds different than what you're running into, my A3 usually has the data, it just can be a pain to get it out sometimes.
