Well, since the same thing, more or less, happened to John Hinckley, I'd say the answer is a big yes.
If you're referring to the specific mechanism here (that is, that the appellate court found the guy "too insane to be jailed" after he was convicted and sentenced), then no, it wouldn't happen quite this way. Under our system, once he was convicted, his mental state would cease to be relevant to his sentence (though it might compel a judge to recommend a facility with some kind of treatment availability), so unless the appellate court overturned the conviction and sentence entirely, they couldn't, in any instance I can think of, revisit the issue of his sanity in order to re-open his sentencing.