I think it could work. It'd just need a lot of movie magic to work. Not perhaps the voice bit but I'd buy it. I mean, I buy 2 years passing between Raiders and LC when he aged quite a bit between 80 and 88. I obviously don't think they could make him pass for 20...But I think they could with makeup and some CGI make him look like he was in his 40s.
It's just...Harrison has a very distinctive look, and while he's wooden, his brand of wooden acting is his own. The only actor who came close to getting Indy down besides him was River and there's really not many young actors who are not only that talented, but also look like a young Harrison. I know a new actor is inevitable, but I want to postpone it for as long as reasonably possible.
But I guess we should be happy with whatever we get. The window for a believable Harrison helmed Indy film closed in the early 2000s. In 2002, he could've easily played Indy just a few years older than LC and been believable, and had a good number of plausible action scenes to boot.
TL;DR Blame Lucas.