Not that I've ever noticed. Or at least, closest to that is when he's forced to go along with it because other members of the bat-family think he needs to cheer up/relax.
So as long as Robin doesn't become a massively zealous evangelical-brony, it's all fine.
And of course he'd be vaguely, distantly and disinterestedly approving, because it fits into the unimportant-to-positive slot in his one criteria for judging such things; How does this affect crime in Gotham?
Of course, if the Joker plots a series of crimes themed around the show or something, he might be forced to watch it all in order to outsmart him. (Which would likely be the Joker's dastardly plan all along, to get Batman to watch a show for little girls and overweight man-children. Batman frustrates the Joker by not particularly being bothered by the jibes, being better informed about Bronies and neither hating the show nor getting overly worked up about it.)
No, Robin would totally get into it behind Batman's back. Batman would know, but not really care.