Can raytracing be used to imitate the behavior of light to a higher degree? Raytracing "sees" the pixel on the other side of the screen;
but doesn't this mean the rays traced can be computationally reflected and refracted imitating the properties of actual light?

It'd be exciting if it were possible. Any visual scene possible outside computer graphics will be possible just using physics equations.
You are late by about 35 years. This was addressed in the historical paper "Whitted, T., An improved illumination model for shaded display. Communications of the ACM, Volume 23 Issue 6, June 1980, Pages 343-349", using  ray tracing.



Since then radiosity has been introduced to better deal with diffuse phenomena. Correct physical modeling of the image formation process was discussed six years later in the seminal "Kajiya, James T. (1986), "The rendering equation", Siggraph 1986: 143".