Here is an article that reinforces the legend that Siddhendra Yogi was trained in "vedic" studies in Udupi. It goes on to say that Yakshagana as a sort of "Jogi Pada" existed in Andhra. However it is known that there were Dashavatara melas in Udupi at that time when Narahari Theertha reined. I am guessing it is likely that Yakshagana traveled from Udupi to Andhra. The book claims otherwise. I am bit confused since no author is really objective. All claim originality. It is also true that Andhra yakshagana prasangas as old as oldest available in Kannada or 100 year recent exist.
I find it fit to say that it existed amongst us when we spoke a language that was neither Telugu nor Kannada. It has become what we see today in different parts. However existence of same name and prasangas in Andhra and Karnataka is not that simple to answer. I plan to read one \andhra prasanga using whatever broken Telugu I know and figure out.