Not usually no… If your shock sensor was set to be that sensitive it would be going off when the wind blows too hard. So a tire slowly deflating will typically not set car alarms off.
To have your alarm be aware of people say…standing next to the vehicle and looking in the windows requires an internal (and optional) proximity sensor which is usually an adjustable radar bubble inside the car. You can adjust those to be sensitive enough to detect people looking inside your windows. I used to hate having to install those, not because they were difficult but because of the complaints it almost always generated. Almost anything would set them off… leaves falling onto the windshield, sound vibrations from vehicles, rain…etc… They were and I imagine still are a major headache.
I used to install alarms and remote start and high end audio equipment in vehicles professionally…back when that was the “in thing” in the 90’s basically.