Yes, but not in the form of chatbots.
Among other things, a LLM can be seen as a store which you query and get results from. A chatbot is cute because it formats output text to look like conversation, and the recent applications are nice because the query (now known as prompt) can be complicated and long, and can influence the format and length of the results.
But the cool stuff is being able to link the relatively small amount of text you input as a query, into many other chunks of texts that are semantically similar (waves hands around like helicopter blades). So, an LLM is a sort of "knowledge" store, that can be used for expanding queries, and search results, to make it more likely that a good result seems similar to the input query.
What do I mean by similar? well, the first iteration of this idea is vector similarity (e.g. https://github.com/facebookresearch/DPR). The second iteration is to store the results into the model itself, so that the search operation is performed by the model itself.
This second iteration will lead, IMHO, to a different sort of search engine. Not one over "all the pages" as, in theory at least, google and the like currently work. Instead, it will be restricted to the "well learnt pages", those which, because of volume of repetition, structure of text, or just availability to the training algorithm, get picked up and encoded into the weights.
To make an analogy, is like asking a human who are the Knights of the Round Table and getting back the usual "Percival, Lanceelot and Galahad", but just because the other thousand knights mentioned in some works are not popular enough for that given human to know them.
This is a different sort of search engine than we are used to, one which might be more useful for many (most?) applications. The biases and dangers of it are things we are only starting to imagine.