From my experience it depends on your mp3 player.
I have an mp3 player that ONLY plays mp3s.
You will find that the songs you download from itunes are NOT mp3s, but AAC files. (different type of file)
The AAC files do not play on my mp3 player. However, some newer mp3 players play AAC, WMA files etc.
So in short, I cannot confirm whether or not you will be able to play the itunes files as i do not know what your player is.
But check out what your player can play. I have obviously not been able to test any further, so I am not guaranteeing anything!!!