Is it possible to redshirt a guy that is ineligible?  Thanks

No ... but if he shows up and if you keep his final GPA above 2.8, he can play 4 seasons (meaning he comes back as a 5th year SR).

This is effectively a Red Shirt ... the problem being that he does not do any practice during his freshman year, so he can not grow during his "red shirt" year.  He also does not have to come back, so if he has not getting any playing time in his 4th year, he may decide not to come back for a 5th season.

Once the player comes back for the 5th year, what happens when you click the "redshirt" link for him?

I'd assumed it wasn't even an option (just like the link isn't there for people who have already has a redshirt), but it seems to be.

you can do it at D3.  There are no ineligibles at D3.  And to answer your last question, the redshirt button won't work.