That defeats the purpose.

I think the whole point of a warrant canary is that you have to do something, every week/month, to confirm that you never had to obey a warrant. And (presumably, I don't think it has been tried in courts yet) a gag order can prevent you to speak about a warrant, but it can't force you to do anything, including actively saying that you didn't receive anything.

If it's automated.. the gag order prevents you to stop it, so it might as well not be there.

Nope. If an adversary seizes our servers, we couldn't stop it from falsely reporting that all is well.

If you sign the request w/ a key that isn't present on your servers than it should be impossible for that to occur.

Unless they seize the computer with the key as well

If an adversary seizes your servers wouldn't you have bigger worries like getting them back or complaying with the warrant?