Yes, autofocus will generally still engage on the 60D with that Sigma 18-200mm, even at the long end. In practice, some third-party lenses report themselves in a way that keeps the camera body willing to attempt AF.

However, because f/6.3 is dimmer than the 60D’s stated f/5.6 AF specification, autofocus may become less reliable. You may see slower focus acquisition, more hunting, or failure to lock focus, especially in low light or at close distances.

Your best chance at the telephoto end is to use the center AF point, since it is the most capable point on the 60D and generally performs better when light is limited.