Does it matter? In any scenario with the global collapse of civilization, the last thing anyone is going to care about is bitcoin. Thing that people will care about are food, water, shelter, fuel, medicine, and weapons. No one is going to be focused on making sure they can still broadcast a transaction when they have nothing to eat.

It is possible to sync a node without internet access by using Blockstream Satellite, and it is possible to broadcast a transaction without internet access by passing it a third party for broadcasting via any method you like - mesh networks, radio signals, USB drive, QR codes, over the phone, etc. So yes, you can access the bitcoin network without internet, but the network itself still requires the internet to run. You can't possibly hope to distribute a transaction across all nodes around the world using only radio waves, and blockstream satellite can't broadcast blocks unless they are kept up to date via the internet.