It's easy enough to see for yourself. The next time both moon and sun are simultaneously visible in the sky, trace a line from moon to sun, at right angles to the terminator. This should be a straight line, but it appears curved. The reason, as you allude to, is due to the fact that it is a geodesic on the celestial sphere. The shortest distance between two points on a sphere is not the rhumb line, its a great circle. Until you figure this out, it is a very jarring sight, and I can think of at least one professional astronomer who could not explain it when it was pointed out to her.