I think just about anything with similar chemistry will dissolve into each other. So, I'd count on a lower viscosity oil breaking up grease/oil based crud. It's not the swiftest idea in the world, but I'll still use WD-40 once in a while for the first cut through car grease when washing up the hands.

I'd think hopefully any left over 'cleaner' wouldn't be a worry later, and I think it's better if the piece doesn't look like it's cleaned.