I'm fairly sure that the 60gb had the actual chip inside of it running all ps2 backups and the older (motorstorm bundle) 80gb has the software in it running almost all ps2 games. There is also a 20gb console that runs ps2 games through emulation...I think...
So to answer the original question, no the 40 GB model does not include PS2 compatibility and no you can't install it. It's not a separate piece of software like a game that you can load onto your PS3. You either have it or you don't.
Wikipedia includes a nice matrix which shows all the features of every model (which is where I got the above info).
I have one of the original ps3 consoles with the 60gb hard drive however im fairly sure that it is a Hong Kong model so I get region code errors when I try playing my australian ps2 games or american ps1 games... i still have my chipped ps2 connected so they can still play on there, however it would be more convenient if i could just play them on my ps3... is there any way i can play ps2/ps1 games from other regions on my HK ps3?
i have a 40gb ps3... i hope there is a way to get it hacked to run ps2 games, but i heard that there is a way to hack the 40gb to run ps2 games through hardware but it could effect the ps3 in some stuff...
there´s no way to play ps2 games on the 40gb at the moment. there´s rumors that Sony is going to release an emulator at some point. That´s the only way it will work. Unless the ps3 is hacked(to run unsigned code) and then somebody codes a ps2 emulator.