Such bootlegs exist, but they aren't likely to give you a good feel for what the audience heard. The available technology (particularly that for clandestine, portable recording machines) wasn't able to achieve that. It's better now, but it still often does not give an accurate representation of what the audience is hearing.

As a long-time performing musician (going back to the 70's, not the 60's), one thing that always amazes me when I see performance clips from back then -- no monitors! Part of the inadequacy of the sound systems of the time had to do with what was being transmitted to the audience, but a big part of the problem was that the performers simply could not hear themselves very well.

Also, much of the time the only things being sent through the PA speakers were the vocals, and whatever "bleed" came through the vocal mics from the drums and amplifiers on stage. It really was very primitive by today's standards.