No you can't RS an ineligible.

As Julius said, you can't redshirt an ineligible.  There is something in the FAQ about players getting a medical redshirt for a season, so technically I guess it would be possible for a player to end up as a 6th year senior (with a normal redshirt plus the medical redshirt), although in all my years and seasons of playing HD, I've never seen nor heard of anyone actually getting that medical redshirt.  Not even sure it really exists to be quite honest.  Maybe someone else has had a player receive one? 

Between the drop of the threshhold for the game considering players "able" to play to 60, the insanely rare instances of significant injuries and the fact a player would need to draw 2 or 3 of them in a single season (knock on wood, but my entire teams have never had 3 significant injuries in a season, much less a lone player...), I would rank the odds of it happening somewhere around my odds of holding a jackpot-winning MegaMillions or Powerball ticket this weekend.

I don't think they ever added the medical redshirt to HD...I know the FAQ hasn't been updated in a while but...

Any given player can only be "redshirted" once in his career (and possibly another medical hardship year to be added in a later release)