Actually, the Tinker app can’t do cloud interaction without the internet either. For connecting your Core however, no internet access is required. You do need to be connected to the relevant router, and have those credentials on hand.
I’ll try a (REALLY REALLY) simplified explaination of the connection process: when you use the app to connect your Core, the credentials get sent out in tiny packages. These will float through the ether to the router. The Core is able to pick up these packages, combine them, and decrypt them, thus recreating the credentials. It then uses those to connect to the relevant router.
Seeing as the Core need to pick up those packages, you won’t be able to do that over the internet (not to mention the fact that the Core would have to be in listening mode to be able to add credentials).
May I ask what the use case is you’re preparing for? Perhaps there are viable alternatives which you haven’t yet thought of?