The QHN/Kollsman window setting only affects what is displayed to the wetware. When you strip away all that the autopilot is just servoing to a pressure altitude. But sure if you are flying below the transition altitude and are flying between areas with different QNH settings when you adjust the setting the autopilot will climb or descend as needed because you told it to servo to a different pressure altitude.
There are many EFB (e.g. Foreflight), or log book, or other flight recorders you can use on an iPhone. And some can record the pressure transducer in the iPhone to record an approximate "pressure altitude". e.g. Naviter SeeYou Navigator intended for gliders can do that (but it's not unusual for modern gliders to have an array of sophisticated air data sensors and specialized variometers and flight computers that would feed the app this data over Bluetooth). Popular EFB software Foreflight will not use the iPhone pressure transducer, if you want pressure data there you need to drive that through an external interface like a Sentry ADS-B receiver that has a pressure sensor built into it -- or much better if the aircraft is equipped with ADS-B Out can receive the "own-ship" ADS-B Out broadcast pressure altitude from it's high accuracy encoder). Any in-cabin pressure traducer will be sensitive to the difference between calibrated static pressure and cockpit pressure, things like opening or closing vents, or varying the airspeed significant (and ram air pressure or suction on the cockpit exit vents) can cause observable changes. And when using an iPhone or similar, especially without a great GPS satellite overhead view (e.g. in high wing aircraft) you are likely not to get high-quality GPS altitude data. think best case ~ +/- hundred feet, worse case with little overhead GPS sat view, much worse... but those consumer GPS app is likely to happily display multiple decimal points of precision :-)
There are many EFB (e.g. Foreflight), or log book, or other flight recorders you can use on an iPhone. And some can record the pressure transducer in the iPhone to record an approximate "pressure altitude". e.g. Naviter SeeYou Navigator intended for gliders can do that (but it's not unusual for modern gliders to have an array of sophisticated air data sensors and specialized variometers and flight computers that would feed the app this data over Bluetooth). Popular EFB software Foreflight will not use the iPhone pressure transducer, if you want pressure data there you need to drive that through an external interface like a Sentry ADS-B receiver that has a pressure sensor built into it -- or much better if the aircraft is equipped with ADS-B Out can receive the "own-ship" ADS-B Out broadcast pressure altitude from it's high accuracy encoder). Any in-cabin pressure traducer will be sensitive to the difference between calibrated static pressure and cockpit pressure, things like opening or closing vents, or varying the airspeed significant (and ram air pressure or suction on the cockpit exit vents) can cause observable changes. And when using an iPhone or similar, especially without a great GPS satellite overhead view (e.g. in high wing aircraft) you are likely not to get high-quality GPS altitude data. think best case ~ +/- hundred feet, worse case with little overhead GPS sat view, much worse... but those consumer GPS app is likely to happily display multiple decimal points of precision :-)