This TAS says hiUnfortunately, this doesn't work with Sonic. In the later games the major offenders are loops, but in Sonic 1 there's varied reasons why Sonic can't pull it off:
* The aforementioned 10 ring box in Labyrinth 2
* In Marble 2 you have to fall through a gap at the start with two rings in it - you can't dodge them both
* Spring Yard 3 has a few rings you can't dodge in one of those tubes with springs at the bottom. The similar one in Spring Yard 1 can be skipped by bouncing off absolutely everything at the start, apparently (I've never done this myself)
* The Scrap Brain 1 trick doesn't work because you can't get to the bottom quickly enough (and I think Sonic 1 handles offscreen rings differently to the Knuckles hack in any case)
I have an old topic somewhere detailing what we thought were the best possible results with Sonic (though it would be obsolete now as I'm certain SB2 can now be done ringless).