I doubt it'll have much of an affect, it's quite rare a block is found at the same time given a high nonce.

If you try opening a command lnie and pinging the main node, if you get a response in less than about 20 ms then it really shouldn't affect the ability to publish a block. If you plan to leave the nodes on their own for a while you might want a failover for the bridge just in case it goes down, that might be your biggest problem.

Yor nodes are technically still connected to the internet anyway so I don't think you've completely blocked that with this setup (unless you did something more advanced - but I'm not sure how that would work).