YESPerhaps, they can. My sister ran a f.lux like app (Twilight) for a while, now her screen flickers green, shows scan lines, and shuts off randomly while dimming the screen.
However my friend ran it for over a year and had no issue. Proceed with caution.
I have chosen to use twilight most nights, as my eyes are worth more than my phomephone screen.
Edit: I wrote this in 2015 -- it's now 2017 and I chose to use screen dimming apps every day since. Well, still no problem, phone runs fine. Not sure why my sister's phone had issues. Out of caution I did delete twilight and started using the built in android blue-light filter.
EditEdit: It's now 2019 and screen dimming apps are ubiquitous on all OS's and platforms, I think it's safe to say they do not damage screens. My sisters phone must have been anomalous.