Do conjugated polymers absorb very low energy photons?
In principle yes, longer conjugated regions absorb at longer wavelengths. The simplest model when thinking about this is to consider a particle in a box, or on a ring if considering cyclic conjugation as in the chlorophyll's. However, in very long polymers, such as polyacetylene, the conjugation length is in fact rather small, approx 10 to 20 double bonds. Nanometer thick  films appear brown and absorb below 800 nm ish whereas if the conjugation length were very large, as per the chemical structure you draw, the molecules would absorb to longer wavelengths and appear black.

This limited conjugation is due to two things, first the molecules are  twisted and bent in forming the polymer and these distortions alter the electronic properties just enough to shorten the conjugation length. Second even when this twisting etc. were removed there are two ways of arranging the double bonds depending how you start. At their junction these two forms form what is called a 'solition' or 'topological kink'  and this is  a non-bonding electron between two regions of conjugation. This also limits conjugation.