Is a successful performance more important to the audience than an authentic one?

With this I would think that the answer lies in what kind of taste the audience as a whole has for music. I would think that the need for authenticity in a performance is trumped by that of the success of the performance. Whether or not a performance is authentic, if it was not successful, the audience will not like it as much as they would if it had been successful. So the conclusion would be that a successful performance is more important to the audience than being authentic.

Is it possible to have an “authentic” musical performance?

I suppose the answer to this would depend on your definition of authentic. A Google search gives five examples of definitions: 

1. of undisputed origin; genuine

2. made or done in the traditional or original way or in a way that faithfully resembles an original

3. based on facts; accurate or reliable

4. (in existentialist philosophy) relating to or denoting an emotionally appropriate, significant, purposive, and responsible mode of human life

5. (of a church mode) compromising the notes lying between the principle note or final and the note an octave higher

So then based on this, the performance should be genuine, traditional, original, and, accurate. If these are the criteria, then I would say that it is possible to come close if you base it on the performance. All of these words could be used to describe a performance, making it authentic by this collaboration of definitions. Using the instruments; how they look, sound, and are played, may give you a different answer. The instruments could look authentic, genuine and, accurate, but may not be made of the same materials as the original and traditional ones. Does that hinder the performance's authenticity? What if they don't sound the same? Then again, I'm sure that if a musician is going for an authentic performance that they would get authentic instruments; ones made of the traditional materials. If the instruments did not sound the same, then I would certainly not call the performance authentic because sound is the most important part of the musical experience. So in my opinion, as long as the performance looks and sounds authentic to the piece that is being played, it could be considered authentic.