Yeah, I didn't hear anyone calling me names.
Does 1password let you use the local copy if you are connected but your login credentials are no longer valid? - no idea. The other questions are answered below.
1Password uses the term vault to mean a particular collection of credentials. In 1Password, I have many vaults for different purposes. All of the those vaults are visible and usable within the 1Password application without a connection to the internet.
When you connect after being disconnected changes are pushed up. I tested by modifying an item, deleting an item, and adding a new item, all while disconnected (blocked by Little Snitch). None of the changes showed on my phone. Once I allowed the connection all pending changes were synchronized to the servers and subsequently showed up on my phone.
While disconnected, 1Password shows a small cloud with a strikeout indicating the lack of connection. When you try to connect, or first start up the app without an available connection, 1Password briefly shows a popup at the bottom of the application:
View attachment 2584989
I was not allowed to create a new vault while disconnected, but could work with my existing ones. Also, once I deleted an entry when disconnected, that entry did not show up in the "recently deleted" category until I reconnected with the server. So, it might be hard to recover an accidentally deleted entry. Once I connected to the 1Password server, the entry that I deleted did appear in the "recently deleted" category.
So, my tentative conclusion is that 1Password's local vaults are fully functional, but the application in total has some limitations.
I do not have any evidence that a user can game this by cancelling their subscription and using the 1Password application permanently disconnected. I also think that if you don't have a subscription to their service you are no longer granted a license to the software.
When someone says 1Password has no local vaults, they might be right or they might be wrong; it depends on their definition of vaults. If you keep the definition of vault simple (an encrypted storage of credentials), then 1Password has local vaults.
When someone says 1Password's local storage of credentials is a cache, they might be right or they might be wrong; it depends on the definition of cache. I suspect 1Password's local vaults are as much a cache as my Dropbox folder is, where all content is forced to be available offline. The more I think about this particular topic the more I realize that it's a technically subtle issue and well out of scope.