The whole point of OFF_CHAIN txns is that you DON'T need to be connected to the network ( ON_CHAIN ).
that
could be a goal of some off-chain mechanisms, but the primary goal of off-chain transactions is moving transactions
off the blockchain---no need to store them or wait for miners to publish them. lacking internet is a whole different issue.
Neither of these touch the network (require you to be online), until someone wants to cash out.
You don't need to be online to sign / verify / swap a TXN.
sure, you can update state that way (assuming you have an open channel). both parties just need to sign. i think the problem is, how do you protect the state of your channel when your not connected? i don't want my life ruled by timelock.

as ETFbitcoin says, you'd only want to do this with timelock expiration far in the future---in case of unexpected circumstances. no matter what, it will always be safer (and less headache) to control good old UTXOs. i like the idea of opendimes, etc as bearer bonds---good for offline transactions.