Yes, you can do the math. But "practical" intuition gives you a good sense of possible orders of magnitude, though, sometimes fails.
A compass needle is easily moveable by hand. Even Lenz effect forces (when only driven by magnets) are weaker than the attraction forces of the same magnet (depending on the speed, of course) though going east->west the flux doesn't change much.
So my conclusion is that, even though it might have had a small effect on it, absolutely not enough to make it change velocity significantly.
A compass needle is easily moveable by hand. Even Lenz effect forces (when only driven by magnets) are weaker than the attraction forces of the same magnet (depending on the speed, of course) though going east->west the flux doesn't change much.
So my conclusion is that, even though it might have had a small effect on it, absolutely not enough to make it change velocity significantly.