Sounds like it could work but the mint would know that a channel is being setup and it would have to track all that state as well (which should incur fees for the service).
Our modus operandi is that the mint should know as little as possible about what's happening between users and that most complexity should be offloaded to clients to keep the mint simple and easy to run. It also decreased the anon set if the mint can differentiate the different usage patterns of users.
My sketch above has only two interactions with the mint: open the channel (the mint doesn't know that this is a channel yet because it's blind-signing) and close it (at which point the mint knows it was a multisig coin with second spend path which is a timelock).
