Here's a bit of an interesting find. Someone over on the Gamefaqs board is saying one of their videos on YouTube received a copyright claim from Nintendo. This video was originally uploaded in 2009 and is nothing more than the original Super Mario Bros. theme in its classic NES style. Not that big of a deal at first, but the claim itself said it was for "SuperMarioOdyssey Audio_01". That would certaily seem to indicate that the classic-style tune will appear in Super Mario Odyssey in some way! Thanks to Andre for the heads up!
Could just be Youtube's automated copyright system being stupid again.
The theme is in all 3d Mario games in some form and that one has 8bit sections. It would be surprising NOT to find it in here.