Can you only play as Sonic in the one-player mode of Hedgehog 2?

That's incorrect! While Sonic is the main character in Sonic the Hedgehog 2, you can actually play as Tails in the single-player mode. You unlock Tails after completing the game with Sonic.

So, you don't have to stick with Sonic the whole time! You get to experience the levels with a different perspective and playstyle using Tails' abilities.