It can be done through filtering, but it's really hard to make it look good. A person named Psiga made this mock-up for Secret of Mana in Photoshop that has always astounded me: https://sites.google.com/site/psigamp3/PhosphorSimTest1.jpg
Unfortunately, no one's been able to figure out exactly how it was made to replicate it in software. But something like it would really add a lot.
There are however really good CRT simulation pixel shaders, such as CRT-Royale: http://emulation.gametechwiki.com/index.php/CRT-Royale