So Star Wars Battlefront 2 got its Multiplayer rebooted on PC through Steam. Can you connect to a server hosted on PC with your Xbox 360 or Playstation 2?
I am quite certain cross-play between PC and consoles is not possible for Star Wars Battlefront II. It certainly was not when the official Online Multiplayer was still operational and it would only be possible to have changed if the console versions got an update, which they didn't.
However, you can still play online with consoles, using the community project SWBFSpy. This projects re-enables Online Multiplayer for the PC version (without Steam or GOG) and also for the PS2 version. I am unsure whether it does for the XBox 360 version.
Further information about SWBFSpy including how to install it for the PS2 version can be found here on SWBFGamers.com. Specifically for the PC version you can find more information in my reply to another question, summarizing the options to play the PC version of Star Wars Battlefront II online.