I don't think so.
To be clear, we have always attempted ASI, and it has intrigued philosophers, neuroscientists, engineers and even the lay person.
It took human life millions of attempts before we became the modern human.
With LLMs, we are on attempt number 1000. To be clear, the requirements for ASI are lesser than the human mind and we have more clarity on what is required as compared to evolution which was a purely production-level iterative process.
For example, we don't expect to micro-optimize LLMs the way the human mind is, which operates on 20 watts of energy.
But it does have a higher memory requirement. A human being can technically hold 40x more data than an LLM is trained on (I don't think this is true, by the way), and this will be a differentiating factor - I am sure we have systems to optimize how this information is surfaced, and an LLM approaches it differently.
For this reason, I struggle to believe LLMs will become ASI, but I think they'll play a crucial part in allowing true ASI to be developed -- which means it'll be able to model new ideas based on old ones and self-improve without depending on programming. I'd love to take out all engineering data, set an ASI back to the 1800s and have it develop the modern computer from there. I think the fundamentals would look quite different.