Splash and Star Tours both have height requirements of 40 inches. So no, absolutely not, the baby won't be able to go on at all. Therefore, learn about Rider Switch (or baby swap, child swap, etc) unless grandpa is willing to stay with baby and not ride on many rides!
The CMs can ask you (er, tell you) (and when I say "you" I mean your daughter or son in law or you too!) to take baby out of the sling for any no-height-requirement rides. I didn't have to take DS out at all, but his first trip he was in a mei tai, on my front, facing me, and was VERY secure. Don't get me wrong, I feel that a properly worn sling is just as secure, but people who aren't sling-knowledgable have the whole Baby Bjorn thing in their head, and I've read on mouseplanet that the CMs are happier with the Bjorn-style carriers than cloth slings (I guess they don't know that plastic buckles can break?). Whatever!
But unless you get a CM like that, you might be able to wear baby on Peter Pan, the "dark" rides like Snow White (extra benefit of baby on those rides...they don't know that it's scary!!!), railroad, HM, Buzz, Pirates... basically anything without the height requirement. But again, the CM might not allow the sling at all, so be prepared for that!