What is an Xbox 360 Arcade Console?

I know this game doesnt have a hard drive, but can this console still run all normal xbox 360 games and run xbox live?

 

It will run all 360 games.

Some games though you won't be able to save your progress.

HD's can be found pretty cheap.

 

I'll be able to play Modern Warfare 2 Online?

 

google is your friend.
the arcade is just a normal 360 without a hard drive and other stuff. it can do anything that a normal 360 can do without the hardware that isn't included.