Perhaps not, but what is the impetus of discovery? Is it purely analysis? History is littered with serendipitous invention; shower-thoughts lead to some of our best work. What's the AGI-equivalent of that? There is this spark of creativity that is a part of the human experience, which would be necessary to impart onto AGI. That spark, I believe, is not just made up of information but a complex weave of memories, experiences and even emotions.
So I don't think it's a given that progress will just be "exponential" once we have an AGI that can teach itself things. There is a vast ocean of original thought that goes beyond simple self-optimization.
Fundamentally discovery could be described as looking for gaps in our observation and then attempting to fill in those gaps with more observation and analysis.
The age of low hanging fruit shower thought inventions draws to a close when every field requires 10-20+ years of study to approach a reasonable knowledge of it.
"Sparks" of creativity, as you say, are just based upon memories and experience. This isn't something special, its an emergent property of retaining knowledge and having thought. There is no reason to think AI is incapable of hypothesizing and then following up on those.
Every AI can be immediately imparted with all expert human knowledge across all fields. Their threshold for creativity is far beyond ours, once tamed.
So I don't think it's a given that progress will just be "exponential" once we have an AGI that can teach itself things. There is a vast ocean of original thought that goes beyond simple self-optimization.