Not if you have to render them, or store them in a font. There are now color fonts.[1] Firefox and Microsoft Edge now support them. It's done with SVG artwork inside OpenType font files.
> Not if you have to render them, or store them in a font.
I think you misunderstood the comment to which you replied. What it was saying is that emoji fitzpatrick scale and color fonts are orthogonal concerns, you can do skin tones in grayscale.
There are multiple ways to encode colors in OpenType fonts: not only SVG (which is probably the least common way), but also the Microsoft COLR table and PNG raster glyphs (used by Apple).
I think you misunderstood the comment to which you replied. What it was saying is that emoji fitzpatrick scale and color fonts are orthogonal concerns, you can do skin tones in grayscale.