Yes, an ENS domain can be updated to point to a new address if a new contract needs to be deployed for updated business logic or code fixes. However, the data storage of the old contract will stay with the old contract.
To prepare for this possibility, it would be ideal to code the original contracts to have some sort of "freeze" functionality, where the contract can be put into a locked-down, read-only state. Then any new contracts could point to the older contract (a "parent"), and could include logic to read the old/existing state off the older contract (using its public access methods), as a means to bootstrap the data of the new contract.
The MiniMeToken takes this idea (though without freezing the original contract), by having logic that if a query transaction is looking for data further back than the history of the current contract goes, it knows to go to the parent contract to look up that history.