The vast majority of the core function and even ability to understand your prompts comes from the training data. With live crawling it can add extra data just like it could have been put into a prompt. Its ability to process and understand what it crawled is, however, entirely based on the core AI.
That means all of the limitations of current levels of AI remain present, including the ability to hallucinate, when live crawling, exactly as it can hallucinate still even when you type all the data you want it to use into the prompt.
I explain exactly why this is in more detail in my reply to you at Live Crawling Versus Plugins - #4 by Ammon