No, AFAIK, they do not. Of course, that would put them into the UV region and we do not routinely measure there. My tests and ours at work normally ran from 400 - 700 nm. However, IR dyes that sensitize AgX at 800 - 900 nm do not show secondary peaks at 400 or so, and I am basing my assumption on these longer chain examples as well as the more common dyes.
Symmetry is not needed as much as conjugation, that is the double bonds shown. Symmetry is often there because a given molecule is easy to make.