I think their most effective move would be to black out google.com search, because that's what most people see. I see diminishing returns in shutting down their advertising and enterprise services.
I don't see how the API's would be affected in any way. They wouldn't shut down all their servers to do this. They'd just have to take down their home page and replace it with something else, like a message against SOPA. Only Google.com users wouldn't be able to use it.