No, they really don't. That's not how they work. At least, not if the "information" you're talking about is real semantic content that real minds can process.
Every piece of information you think an LLM has access to is actually just converted into a stream of additional tokens that are fed into the model to (hopefully usefully) modify the next tokens it predicts. That's not the same thing as having actual access to information. Tokens are just numbers with statistically more (or less) likely relationships to each other.
I'm not trying to downplay LLMs. They're architecturally interesting and have genuine uses. I'm just trying to head off a bit of technical inaccuracy.