Meaningful questions. A few quick thoughts ... from what I recall dyes are used to produced color in anodized aluminum. Pure black will absorb all visible wavelengths, however (1) dye that looks black will most likely reveal a different chromatic absorption spectrum if a prism or similar thing is used to view the light that bounces off it (2) even if the dye is a perfect absorber of all visible wavelengths it won't much matter unless the fins get way hotter than you would hope they would get - a stove burner doesn't begin to glow visible red until it is much too hot to touch (3) the thermal conductivity of aluminum oxide is only about 1/8 as great as the thermal conductivity of pure aluminum, so by anodizing it you would in effect be coating it with a thermal insulator (4) an object that absorbs all visible wavelengths has properties akin to a "black body" but is not necessarily a "black body" in the sense used by physicists.
The concept of a "black body" is defined from the perspective of absorption, denoting an ideal (i.e., hypothetical) object that absorbs every quanta of incident EM radiation irrespective of wavelength or incident angle. If particularly-defined equilibrium conditions are met a black body will reradiate the energy it absorbs. Since the thermal energy that is desired to be radiated from the heat sink is predominately long wavelength (longer than visible wavelengths), if the heat sink fin were a true "black body" it would be somewhat analogous to using an RF amplifier for audio. "Black body radiation" refers to radiated EM energy wherein the spectral makeup is that of an ideal "black body" at some specific temperature, i.e., the spectral distribution obeys the mathematical formula discovered by Max Planck.
WARNING: the following train-of-consciousness discussion of the historical roots of quantum physics is intended only for people who are not annoyed by other people's train-of-consciousness discussions of the historical roots of quantum physics.
The black body concept and related concepts are interesting because quantum physics has its historical roots in the effort by physicists to explain why hot objects do not radiate energy in a manner uniformly distributed over wavelength, i.e., why the color of a hot object changes from red to white to blue as the temperature increases. As far as anyone could figure out, as the end of 19th century was looming near, there wasn't any reason why a hot object ought not emit white light (uniformly distributed over wavelength) that merely increases in intensity as the temperature increases. Max Planck figured out the statistical formula that matches the experimentally observed spectral distribution. His formula "explained" why the emitted radiation was predominately long wavelength (red) at low temperature and why the spectral balance gradually shifted toward shorter wavelength as temperature increased. But why did nature favor that mathematical distribution, asked everyone. Someone, presumably Planck, pointed out that the only way the formula could be explained would be if energy were only radiated in discrete chunks, i.e., quanta. At low temperature, comparatively few short-wavelength quanta are possible (compared with what is possible at higher temperature) because short-wavelength quanta carry off a lot more energy than long-wavelength quanta. The idea that energy consists of discrete quanta was so radical that not many physicists were bold enough to say that this really did mean what it meant. Another major problem that physicists had been trying to explain was the photoelectric effect. In particular, why it was that low-intensity UV light could stimulate electrical current but a high-intensity red light could not, no matter how great the intensity. Einstein used Planck's theory of black body radiation to explain the photoelectric effect and was awarded a Nobel for the explanation. (He was awarded a 2nd one for his theory explaining Brownian motion, which settled the question of whether atoms were real, which question was still unsettled at the start of the 20th century. He was never awarded a Nobel for either of his two theories on relativity. The first theory of relativity, the explanation of the photoelectric effect, and the theory of Brownian motion proving the existence of atoms were all published the same year, 1905, while he was still working as a patent clerk.) Einstein explained that quanta of red light don't carry enough energy to make orbital electrons take the leap from one atom to the next atom, and that when intensity is increased, this only increases the quantity of quanta that are too weak, whereas individual quanta of UV light individually possess enough energy to make it happen. The next major player was Bohr, who realized that the quantum nature of energy was the reason that the elements all had their very particular and unique absorption spectra. This insight along with years of determined effort permitted him to come up with his atomic model where electrons orbit not in an any-orbit-is-as-good-as-another fashion (a Newtonian, planetary fashion) but rather in a fashion where only certain particular orbits were permitted, each with its own particular energy level, such that the energy difference for an electron jumping from one allowed orbit to another allowed orbit matched the energy of the emitted/absorbed wavelengths of an element's emission/absorption spectrum. At some point someone pointed out (maybe it was Bohr but I don't recall) that if you apply Einstein's most famous formula to the mass of the electron to obtain the equivalent energy and then apply Planck's constant in the equally routine manner to that amount of energy, thereby calculating the electron's physical wavelength, that the allowed orbits in Bohr's model are those orbits where the circumference is an integer multiple of the electron's wavelength, such that an electron orbiting an atomic nucleus may be considered to be a sort of standing wave. (The orbital circumference is a trivial Newtonian calculation using the electron mass and kinetic energy.) Interesting it is that for electrons moving through space the particle model is ideal whereas electrons that have been captured by an atomic nucleus are best modeled as standing waves.
You were warned not to read past the warning.