Would the night sky still be dark with 2mm-sensitive eyes?

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If human eyes were sensitive to electromagnetic radiation around 2 mm, the night sky would not appear dark due to the presence of the cosmic microwave background radiation. This radiation is omnipresent, meaning that wherever one looked, they would perceive the microwave background. The visibility of the sky would also depend on the sensitivity of these hypothetical eyes to microwave wavelengths. Additionally, the atmosphere is relatively transparent at 2 mm, which would allow for clearer visibility of this radiation. Therefore, the night sky would likely appear illuminated rather than dark.
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Would the night sky appear dark if our eyes were sensitive to electromagnetic radiation with wavelength around 2 mm? Why or why not?
 
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Thats the peak of the microwave background - so where ever you looked you would be seeing uwave background. Depends how sensitive your uwave eyes are!
Incidently the sky is fairly transparent at 2mm.
 
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