Theory predicts that global economic growth will stagnate and even come to an end due to slower and eventually negative growth in population. It has been claimed, however, that Artificial Intelligence (AI) may counter this and even cause an economic growth explosion. In this paper, we critically analyse this claim. We clarify how AI affects the ideas production function (IPF) and propose three models relating innovation, AI and population: AI as a research-augmenting technology; AI as researcher scale enhancing technology; and AI as a facilitator of innovation. We show, performing model simulations calibrated on USA data, that AI on its own may not be sufficient to accelerate the growth rate of ideas production indefinitely. Overall, our simulations suggests that an economic growth explosion would only be possible under very specific and perhaps unlikely combinations of parameter values. Hence we conclude that it is not imminent.