I don’t have Minion Pro to test this, but you can set the character active with
newunicodechar, look up whether the current font contains
\iffontchar, and return the character if so, e.g.
In practice, you might want to wrap this further in
\ifmmode to use
\varrho in math mode, e.g.
You hit on using Gentium as a fallback font, instead of ρ as a fallback glyph, which is a great idea. You might want to load the supplemental font with
Scale=MatchLowercase so the letters come out the same size. Also be sure to enclose the font change in a group, so it does not bleed through to the following text.