Regrinding can't hurt your grinder, and on most designs, won't foul it either (I'd recommend taking the hopper off afterwards and looking around to make sure).
I have no idea as yet how it will affect grind distribution. My point is simple -- a cheap grinder that can't grind for espresso from whole bean in one pass can often do so in two passes. I was speculating that a grinder that could grind for espresso in one pass, but did so inconsistently, may show improved in consistency when used in two passes.
The Eureka MCF is one of the most rebadged, i.e. popular with espresso machine manufacturers, grinders in Italy. I've used it side by side with the Mini in informal tests, and could detect no difference. If by double grinding, you get improved consistency from it, or a more controlled expression of acidity and bright bitters, that would be news indeed.