#Not unless life evolves *extremely* quickly.

There are two conditions for the cosmic microwave background to be able to support life:

 1. It emits strongly enough at wavelengths required by photosynthetic pigments.
 2. It's bright enough to transmit a useful amount of energy to any life out there.

If either of those conditions is not met, life cannot survive (as the first stars will not be born for another 100 million years or so, there isn't another feasible energy source). It turns out that any photosynthetic life forms on your planemo will only have a few million years in which to evolve - not nearly enough. If they were magically transported there from the future, they might have a chance, but not if they formed *in situ*.

##Temperature

Let's first see what limits we can place on life based on the evolving temperature of the CMB. It makes sense to talk about the cosmic microwave background in terms of its redshift. For instance, as we look back in time, the temperature of the CMB is
$$T(z)=T_0(1+z)$$
where $T_0\approx2.725\text{ K}$, its approximate temperature today (at $z=0$), and $z$ is the redshift. Similarly, [the relationship between the age of the universe and redshift](https://books.google.com/books?id=CQYu_sutWAoC&pg=PA77&hl=en#v=onepage&q&f=false) is approximately
$$t(z)=\frac{2}{3H_0\sqrt{\Omega_M}}\frac{1}{(1+z)^{3/2}}$$
where $H_0$ is the Hubble constant today and $\Omega_M$ is the dimensionless matter density of the universe.

Now, the CMB was released during recombination, where $T\approx3000\text{ K}$. This corresponds to a redshift of $z\sim1100$, and thus an age of about 375,000 years. Now, 3,000 Kelvin isn't much  - it's about half the surface temperature of the Sun. That means the radiation peaks at a wavelength of $\lambda\approx966\text{ nm}$, which is already outside the visible spectrum. [However, the CMB will still consist partly of visible light](https://physics.stackexchange.com/a/126133/56299) until it reaches the [Draper point](https://en.wikipedia.org/wiki/Draper_point), which corresponds to an age of 2.7 million years. Given that photosynthetic pigments on Earth are largely sensitive to visible light - which will only compose a small part of the CMB, even after it's emitted - it seems that after a few million years, they'll be out of luck.

##Energy density

Since the cosmic microwave background is (approximately) a black body, we can [analyze it in terms of Planck's law](https://physics.stackexchange.com/a/480409/56299). [Andersen et al. 2018](https://arxiv.org/abs/1801.03278v1) actually did this for the CMB at various times in the early universe, and determined what it would look like to a human observer. They found that it was actually *too bright* for human eyes up to 1.2 million years, and too dim after 5.3 million years - roughly twice as late as our simple calculation of the Draper point.

We can use this as a proxy for how photosynthetic organisms would receive radiation, given that green, chlorophyll-rich plants thrive in the same environments humans do. It seems unlikely that they could survive far beyond 5 million years - again, assuming that they're similar to the planets we have on Earth. If we consider exotic photosynthetic pigments that operator well at far longer wavelengths, perhaps things could be a little different.

##The impossible planemo

Something that I've ignored up until this point is that your planemo can't exist at all at this point in the universe. It would be composed of heavy elements and silicate compounds. Unfortunately, those compounds can only form after the first stars in the universe - Population III stars - are born and die (which, as I said before, should happen about 100 or 200 million years after the Big Bang).

Indeed, galaxies as we know them won't yet have formed even by the time the background radiation becomes too dim for significant photosynthesis to take place. Structure formation takes quite a long time, and when the universe is a few million years old, galaxies are still far in the future. Overdensities exist, and those overdensities will eventually collapse into protogalaxies and then galaxies, but that's about it at the moment.

I include this only for the sake of completeness; I think we've ruled out the possibility of life even if we handwave away the setting!