I don't think it really needs to be a server. Lightning wallets only need to get online every 2 weeks or so to ensure their counterparty isn't cheating. I think a bitvm wallet could do the same thing. As an (occasional) bitvm dev, I want to ensure my bitvm programs use a 2 week timelock to give users time to (1) open their device and check that the program was executed correctly (2) and penalize their counterparty if they ran it wrong.