You're right, InCopy doesn't have a Load Swatches (nor Save Swatches) command. Can't create spot colors either or access swatch libraries. It's very limited.
You can place a graphic that has the ASE colors in it and they'll be added to the Swatch panel, but only works for spot colors. Process color/mixes are ignored.
If they're CMYK mixes you'll have to recreate them by hand in InCopy's New Color Swatch dialog box. Or you could color text with them and Place the text file.