The Axis Q1615 has a gyroscope, and it uses it for shock detection alarms. I don't think it uses it for tampering alarms, though. Those are based on the scene changing like other cameras.
I think there are other ways to go about this, though. If you're using box cameras in housings, you can add tamper switches or vibration sensors (depends on the environment and the housing) and connect them to an input on the camera, which can trigger an alarm. You can also set up camera tampering alarms in most IP cameras, so if the field of view changes it will alarm. It's not guaranteed to change from someone accessing a camera, but it's another step.
Also, if someone physically disconnects a camera, the VMS should trigger a video loss event, but obviously it's preferable to know before this happens.
As far as HTTP messages, there are several cameras which will do that, but it's not a universal feature. Axis does it pretty simply. I think Bosch does as well.