There are two relevant problems here, I think.
For one, the question for Anthropic is whether LLMs, specifically, not AI techniques more generally, can help significantly with cancer research. And here, all experience so far is that LLMs only really work when they can easily automatically verify their own outputs and self correct - such as in math (using automatic proof verifiers) or programming (using compilers and unit tests).
The second problem is that biological research speed is highly dependent on slow biological processes, such as cultures and long term studies. In programming, if an LLM could provide excellent insights and research suggestions 100x faster than a human, it would speed up the work roughly 100x. But in biology, it would only speed up the total work by a small amount - as any insight, even if absolutely brilliant and spot on, would still require months and years of actual experimentation.
For drug discovery, you can simulate interactions in silico, driven in an agentic loop via LLM. Mostly stil using non-LLM tools, of course, but it saves time.
If I was Dario, and I was after a cynical sales grab to go with the "actually curing cancer!" spiel, I'd probably aim for a drug repurposing strategy. I'd use the above approach to find existing drugs that might target known pathways that drive incurable cancers. I'd only screen compounds with extensive safety data and easy delivery mechanisms, and from the in silico hits, I'd throw a tonne of money at rapidly experimentally screening all those candidates in parallel, and then rapidly push those that worked into clinical trials. I'd assume that, with a small but non-negligible prior, and the money to push through hundreds and hundreds of candidate compounds through at once, I'd have a reasonable chance of getting one drug through to a "Claude Cured Cancer!" show-stopper headline.
But I think even then, with all of Anthropic's wealth, you'd need 2 years minimum to move from initial screening targets to a Phase 3 trial. And it would be an almost criminal waste of research funding to get there -- the dollars for discoveries ratio would be appallingly bad.
(If I was Dario, and I actually wanted to cure some forms of cancer? I'd just use my obscene profits to fund actual cancer research, step back, and let the researchers get on with it.)