The American Bad Ass character only broke "kayfabe" in the sense that the guy wasn't playing a monster anymore. He was still playing a character though, even when he was sitting in on the Kimmel show and pretending to be himself. It's not like he stopped being Undertaker while working the Wrestlemania angle that worked in Percy's death. I'm not certain he'd do it to induct the guy into the HoF next year unless he decided he's done rasslin'.
When it comes to public speaking, Hayes, Kane and Foley are a lot more eloquent. Sentimentally, it would be nice to see Taker break character and share something about Percy. The reality is that Undertaker seems to be a very private guy and tends to hold a belief there are certain things that aren't meant to be shared about the business or what goes on off camera.
Regarding whether anyone would care about some name that hasn't been on camera or relevant to most fans for years, the WWE does it all the time with the Hall of Fame. The fact they not only inducted Koko B Ware, but convinced a bunch of "smarks" that he was ever an major player in the business by any stretch of the imagination, much less belongs in any rasslin' hall of fame, is a testament to their ability to sell.