I must say, this is pretty low to do to someone.

That said, when we were training our new person for on-call, I did arrange something like this to happen becuase we couldn't say when a real error would take place. Although after the first night and several legitimate errors, we stopped.

To be truely BOFH-ish, I suppose you could set it so that it would send the page out at random times each night, instead of the same time every night.