As far as I can figure, no.
However it did seem to happen to this gentleman on this YouTube video (warning: this video contains strong language)
Although I am uncertain of the legitimacy of this find. Furthermore, the alleged shiny he found was the unused sprite for Hoppip, a species made the final cut and so is not grouped with the unused beta Pokemon of which you are referring to. This may have a bearing on the fact that it was found shiny when the other beta Pokemon were not, but I cannot say for certain.
I looked at the website for the group who discovered the beta material and found no mention of shiny variants for the beta Pokemon. I think that they, who hacked the game to get such information, would have known about any existing shinies and told us in the case that they were present.
I hope this helped.