I would guess yes, since I can see come noise looking at solid color surfaces or at night, but on the other hand it might be some sort of slight hallucination, it is proven that during sensory deprivation brain may create hallucinations to keep itself busy, the same might be happening here (but on much lower level).
So, is there any scientific research on that matter?
I think maybe no, but possibly yes. But at higher level.
Yes. The retina does produce closed-eye hallucinations, some of which may be due to random firing by neurons due to thermal noise in the retina.
All detectors, of any design, have noise. At least some forms of noise, you can mathematically prove will always be present.
If you look into complete darkness, like in a cave or mine, you will see flashes of light, faint, static-like “snow,” and other visual phenomena. This could all be considered “noise” in the system, some of it comes from your rods and cones mis-firing (what would be analogous to thermal noise from a CCD), some of it comes from your visual cortex trying to do something useful with the limited data stream coming in (which I guess would be analogous to the processor in a camera malfunctioning).
The image we perceive from our eyes is heavily processed compared to the raw data that flows through the optic nerve. Not just processed like how a camera processor turns 1s and 0s into colored pixels, but also like how an editor can Photoshop an elephant into looking like Natalie Portman. I suspect that getting rid of (thermal) noise is a relatively minor part of the processing that goes on in your brain.