Here's my thoughts.

Cheat days have got to be an absolute NO unless you're fully okay with your resolution evaporating into nothingness.

You wouldn't have a cheat day if you were a drug addict. For many people, sugar is as addictive as morphine. Brain scans will actually show this, apparently, in the way certain parts of your brain light up.

If, potentially, you were able to limit cheat days to something like once a year (like, on your birthday, or Christmas), then MAYBE. But it doesn't sound like that's something you could do.