More accurate is shutter speed. In my experience you want a 30 second shutter speed but can work down to 15 seconds. The P4 only goes down to 8 seconds. You are not really going to get a quality milky way shot with this. The other limiting factor is movement. You are just never going to get the P4 to stay still enough to even make stars look very clear... unless you were to mount the P4 onto a stationary tripod.
Let me also say that drones are design to take shots down (or level). I'd think most milky way shots could simply be captured with a normal camera.
At night, even if you turn off the front LEDs I'm guessing the rear blinking greens would be enough to drown out a shot like that. I suppose you could either tape them over or disconnect them entirely.
Also if it's like the existing Phantoms, you'll only be able to pan the camera 30° above horizontal, so no overheads or anything.