An important thing to note is that the mount is not well aligned and initially misses by over ten minutes. But it converges quickly. Also note the offsets are confined to this routine and forgotten when it completes. So the routine should not need state that needs to be tracked and maintained that could affect other parts of the code.
If you do want the ra dec values reported by the mount to be accurate you can do a single sync when it completes. But some mounts don't interpret sync in the intended way and the mount still won't report accurate ra dec values. But that won't affect the centering.
Frank