Yes and no.
Usually it’s an operator error, you can buy and download the charts, and at least on Wartsila they might not show up unless you install the licenses separately, It’s not exactly intuitive and has fooled me in the past.
These chart provider programs like One Ocean are pretty robust, it’s like 90% offline. But if you can’t get updates, I don’t think you can get new charts, but I’ve had this work in pre-starlink era, so it’s not the most data hungry, especially when you’re only looking for one port. I mean if the antenna gets blown off the roof completely, When we’re In port I’ll just hotspot the computer from my phone and not tell anyone.
But yeah, worst case scenario you’ve lost internet and your only option is to deviate to Puerto Cabello and you don’t have the charts for it, you’re out of luck. Chances are you’d be out of luck if you were on paper too.
But in the US, I keep a personal backup of the ENCs which can be loaded into an ECDIS or ECS with no license, because they are free, and while they might not be up to date they’re probably close enough for an emergency. I Also keep Open CPN and a GPS for my tablet just in case everything does go to hell, because I for one would like to get home.