Can you attack Time Eater as Classic Super Sonic?
It is as you have said. It is possible to harm him as Classic Sonic, but after an hour trying myself, I found it rather difficult and as soon as I thought I was close enough, I'd have to switch back to 3D space. A good strategy I found while fighting this guy is to just hold the boost button in 3D space, then when he switches to 2D space, try to collect as many rings as possible as, to me, it is easier doing it in 2D space.
That said, this video shows Time Eater being defeated as 2D only, showing that it is indeed possible: