Yes it does. After you finish a character's route, once you start a new story, it will give you the option to turn on or keep each character's "cheat" off.
Moocha - 10x normal production rate
Yolkie - 10x normal production rate
Finn - start the game with 100,000g
Cotton - don't know, but assume 10x production rate
None of the other characters are available to romance right now so I couldn't tell you their cheats either
ETA: you can turn on multiple characters cheats at the same time. So playing a game starting with 10x production rate for Moocha, Yolkie, and Cotton (assuming that's Cotton's cheat) and 100,000g from the start is possible all at once.