Yea, I'm not following
@dmaziuk either. At best, he seems to have confused his physicists, maybe thinking of Newton, not Einstein. But also, he seems to be talking about how to return to a boat drifting in a current, which, of course, is impossible since you can't know the position of the boat.
Theoretically, current shouldn't matter for exactly the reason you described, the INS should continuously add all the acceleration vectors, integrate over time, and know your exact position. My old flight instructor (retired from the Air Force) said his aircraft INS was so good he could taxi to his spot on the tarmac after a long flight. He was prone to hyperbole, but the guy was experienced and an educated engineer and pilot.
But, there seems to be some practical limit to the technology and dealing with currents. The guys at
ARIADNA.TECH Diver Navigation seem to be struggling with current compensation too. In their FAQ, they comment about it. I wonder what the underlying issue might be. Maybe the resolution of the IMU?
"Sea currents can be compensated by activating the sea current compensation function while swimming against the current and maintaining a steady position for a few seconds. The speed and heading of the current are measured and taken into account in subsequent navigation calculations."