Affecting it story-wise, not really...they do award single-player reward crates though (research, items, credits, crafting mats, etc).
They can give stuff like credits, weapons, and materials. So it's nothing that has a meaningful impact of single player.
From the CHEAT HAPPENS FAQ:
Q: Why aren't there any cheats for multiplayer games or modes on your site?
A: CHEAT HAPPENS does not support or condone the use of cheats in a multiplayer environment.