I have no real experience with patient opinions on this subject, so I am not really answering your question directly.
However, I would guess that the average patient would have no idea what the differences in training would really mean. As people in the medical field we know and understand the pros and cons of the training, but a random person off of the street just knows that the doctor is a "plastic surgeon."
I doubt most people would really have a sound understanding of what it means to be a plastic surgeon by going integrated, independent, or through another route like ENT. In the end, the results and recommendations from other patients will likely be far more important than any perceived differences in training.
One problem I could see is if the patient was looking around on the internet and stumbled upon some influential opinions in support of or critical of the integrated system.
that was a lot more than I intended to write, but I think those are some key points that are applicable to your question.