If we only handle AI that well doom is probable. It has economic uses, unlike nuclear weapons, so there will be a thriving black market dodging the safety concerns.
Also there are only a few companies that can fab the semiconductors needed for these training runs.
It is also quite possible for our society to decide that deep learning is too dangerous and to outlaw teaching and publishing about it, which would not completely stop the discovery of algorithmic deep-learning improvements (because some committed deep-learning enthusiasts would break the law) but would slow the discovery rate way, way down.
And most people who think AI "progress" is so dangerous that it must be stopped before it is too late have loose confidence intervals extending for at least a couple of decades (as opposed to just a few years) as to when it definitely becomes too late.