As regards any flavor molecules making it through distillation, I ran across something possibly related. A YouTuber who posts as "Big Clive" used a water distiller (single stage) on supermarket Scotch.

https://www.youtube.com/watch?v=zfJjicQkYsU

According to him, there was still some flavor in the distillate.

That said, I think you might be spot-on with mouthfeel. The only question that remains is whether that mouthfeel would still exist if the vodka is mixed with anything (particularly something carbonated).

Disclaimer: semi-non-drinker here who can't remember the last time he had a taste of vodka.