It actually may work. But not because aliens will come to save us - there is no time. But because any signal we send in space will reach any star before intelligence explosion wave, and thus aliens may know potentially hostile nature of our AI.
Our AI will know all this, and if it wants to have better relation with aliens, it may invest some resources in simulating friendliness. Cheap for AI, cheap for us.
So imagine you're living like you are, today, and somehow some message appears from a remote tribe that has never had contact with civilization before. The message reads "help! We've discovered fire and it's going to kill us! Help! Come quick!"
What do you do?
I'm not sure how you envision "sending signals into space" as noticeably different from what we've been doing for the last 100 years or so. Any civilization close enough to hear a more directed plea, and advanced enough to intervene in any way, is already monitoring the Internet and knows whatever some subset of us could say.
Desiderata for an alien civ that saves us:
up to y'all whether the intersection of these criteria sounds likely
If a hostile alien civilization notices us, we’re going to die. But if we’re going to die from the AGI anyway, who cares?
Anyone with a p(doom from AGI) < 99% should conclude that harm from this outweighs the likely benefits.