With the understanding that color refers to the visible portion of the electromagnetic spectrum, do wavelengths outside the 390-700nm range possess a similar attribute, or are they "black", and devoid of any such property?
"Color" is not a property of visible light; visible light has only wavelength and polarization, and all photons have these properties, but no photons have any special property of color.
"Color" emerges from our perception of light. Light stimulates photoreceptors in our eyes, which in turn sends signals to our brains. Most humans have three different photoreceptors in their cone cells (cells in your retina specialized for color vision). Light of different frequencies stimulates these photoreceptors to different extents. So blue light will stimulate the first photoreceptor a lot and the second a medium amount and the third a little, and the reverse for red light. Then, by judging the intensity of the signals it receives from each type of photoreceptor, your brain can judge the color of the light entering your eye. So the color is not innate to the light; it emerges out of our processing of the light.
Photons that are outside the visible spectrum do not set off our photoreceptors. This isn't because they lack some special property of color that other photons have. It's just that our photoreceptors aren't sensitive to those frequencies. There is no special color property of any photon, visible or not. There is no physical difference between a photon of visible light and one outside the visible spectrum. Indeed, by boosting to a new frame, we can redshift or blueshift any photon into the visible spectrum.