I played it without ever using save states (except for saving in the sense of like, not having to use a password to get back into the game), and I can confirm, I wanted to kill myself.
I have it both on the original cart and I also own a NES Mini. I've only ever played it on the cart, and boy is that rough. I should really give it a chance with save states on the NES Mini one day, but that is not high on my gaming priority list.
NNID: theRepublic -- Steam ID: theRepublic
3DS - Currently Gaming Like It's 2011 - The Legend of Zelda: Ocarina of Time 3D - Master Quest
Wii U - Currently Gaming Like It's 2015 - Super Mario Maker
PC - Currently Gaming Like It's 2012 - Borderlands 2
Mobile - The Simpson's Tapped Out and Yugioh Duel Links