Answer:
no they do not.
The only playstation that played playstation 2 games. Is the original ones from when it came out, Not true all 4 USB port PS3 play some PS2 titles and some were made well until August 2008 when Production was switched to a PS3 80 GB model with 2 USB ports. The 40 GB model did not Play PS2 games and also had 2 USB ports but they still sold PS3 models that did when selling the cheaper 40 GB models. When the PS3 Slim came out in 2009 they had not been making a PS3 that could play PS2 games for over a year. see related link they stopped makeing them, about a week after selling them and made a new version of it.