I would direct you first to
the TDS for the Grout Refresh product, Jared.
Some years ago we (TYW) tested a handful of such grout "stain" products, but I don't recall if this MAPEI product was among them. In general I found them to be much like latex-based paints, rather than stains. We didn't test them on epoxy grout at all, and I'd be a bit skeptical of such an application, even thought the TDS indicates epoxy grout as a suitable substrate. And no clue as to longevity as the testing was not done on actual, in use, tile installations.
And saving money over removing and replacing epoxy grout? Yeah, but on a surface with "a ton of grout lines," it's gonna take somebody a long, tedious time to paint those grout lines. And to hafta do it again sometime in future? Not sure the customer shouldn't just schedule some therapy that would allow her to embrace the grout color she has.