I see this as very hard to implement. There are several cases that can not be solved.
One way sync could be achieved. But two way isn't possible. The reason is that we can not know if a geocache has been added to one of the sides, or removed from the other.
The next issue is that we can not do this in real-time. It would then have to be daily syncs or similar. Which in my opinion would ruin the use case, and make it too unreliable.
However, I like the idea, if it would be achievable with the API from Groundspeak.