This comes as a comment as I haven't used godot 3's MobileVR yet. But I work with acceleration and gyro sensors to control the camera on Godot 2 and I've just had a look at the MobileVR sources.
1) The default MobileVR Interface should run on iOS and Android with simple VR-Devices. Such as Google Cardboard.
Google Cardboard is some piece of carton with 2 lenses and a place where to put your phone. No extra sensors no motion sensing in the "cardboard" itself. You can configure it to support (similar) devices of different dimensions. It seems that the cardboard "standard" allows devices to come with QR-Codes to automatically configure these settings but Godot can't use such QR-Codes, yet.
Short answer: yes with "google card board"-like devices.
More fancy devices with movement sensors or 3d controllers not yet.
2) There's code for head-tracking in the MobileVR Class and accelerometer + gyroscope is supported.
3) It seems like there's a fallback to the the magetometer (compass) sensors (maybe also a general use of the magnetic sensors). So the Interface might do "something" as long as there are at least acceleration sensors. But: Without a gyro sensor the display might lack (be shaky or wrongly oriented). Also "yaw" rotations (around-y axis) might not be possible if also the magnetic sensor is missing.