No, the search space is tiny: you can just attack 1 BPE at a time! Stuff like password guessing is almost trivial when you get to do a timing attack on each successive character. So that lets you quickly exfiltrate arbitrary numbers of prompts, especially if you have any idea what you are looking for. (Note that a lot of prompts are already public information, or you can already exfiltrate prompts quite easily from services and start attacking from there...)