It is possible to play online on a Ps2 Slim?

last I had heard the servers for the ps2 games are all shut down (much like wii) and online play for games is substantially impossible unless you are doing this on a moded console and have access to a third party server but this may need some challenging home networking if these servers still exist.

there is also the possibility to pair consoles for a system link with ethernet I believe but game support for this would have to be enabled.

homebrew also offers some custom bbnetwork if I recall correctly but I doubt it still running.

homebrew does enable ftp streaming of games so if you are technically inclined you could establish a network with your pc and host files to it so the ps2 is essentially streaming your game to your console over your private network.