Not quite the same. It’ll come out in the wash acknowledges a current out-of-balance but states trust that things will eventually even out. It’s a wash implies that things have already evened up.
Duckles: Thanks for paying for those concert tickets, DoubleJ. How much do I owe you?
Me: Don’t worry about it, it’ll work itself out in the wash.
At a later date:
DoubleJ: It was great to have dinner with you, Duckles. What’s my share of the tab?
Duckles: Don’t worry about it, dinner is on me since you picked up those concert tickets awhile ago. We’ll call it a wash.