Every hotel should have a crash plan. Where I worked, we printed reports ever X hours. In an extended computer outage, the first step involves verifying exactly which rooms are still vacant. That process takes time, as you have to physically check each room. Once you know which rooms are vacant, you can begin doing manual check-ins.

So, the answer to your last question is no. Guests shouldn't end up sleeping in the lobby if computers are down for an extended period. Once organized, running the Front Desk "manually" isn't difficult. It just takes some time to initially set up the list of vacant rooms. Although clearly, some hotels will be better organized than others.