I haven't seen Yorick as a free week champ in 2 1/2 years or so. It could just be that that one time I wasn't playing League for a week or two Yorick was free week; but I've seen people like Thresh being free every 3 free weeks or so. I'm not sure to get Yorick or not because I've never been able to try him out, so if anyone else agrees that Yorick should be a free week champ a bit more please upvote this thread. :^)
Never Free Week -He's purposely not in the free week rotations along with Poppy, because of their "toxic" gameplay, and not wanting to encourage more people to play them. After they're reworked, I bet they'll be put back in. As for trying Yorick, you could watch videos of people plying him and see if he looks fun or try to get / use a PBE account to play him for "free."
I think it's a bit hypocritical of Riot to say "This champion needs changed so bad we're not putting them in the free rotation, but we won't schedule an update for him".
https://support.riotgames.com/hc/en-us/articles/202294884-Champion-Update-Schedule
Poor Yorick, Skarner gets reworked more times than people can remember, but no one at Riot can seem to make you a priority.
