A damaged or removed anti-reflective coating mainly increases reflections at that glass surface. In practice, that can cause more flare, ghosting, glare, light loss, and lower contrast—especially when bright light is in or near the frame.

It usually does not stop the lens from functioning, and on a modern multicoated lens the effect of losing coating on just the outside of the front element is often smaller than people expect. Under normal lighting you may see little to no obvious difference. The problems are most noticeable in difficult lighting, such as shooting toward the sun, headlights, or other strong point light sources.

Also, normal fingerprints or careful cleaning will not remove lens coating; it generally takes improper chemicals or abrasive rubbing to seriously damage it.

So: the lens will still work, but image quality may suffer in challenging light, mainly through reduced contrast and increased flare rather than overall sharpness loss.