While technically it is possible as described above, it makes more sense to me to design a system around a dedicated host "server" that doesn't participate in the game if you need persistence when people connect and disconnect rather than try to create a system that can migrate hosts - you will run into a lot of frustrating design walls if you work that way.
The biggest one is upon a sudden host disconnect, even if you managed to get everyone to rejoin, much of the data that the host was responsible for will not be recoverable, and it will be far from a seamless transition. If you can create a system where the host manually hands off the host role, the transition will be much more controlled and easier to work with.