This really depends on the kind of mp3 player. If you can just drag and drop mp3 / mp4 / wma / whatever files in windows onto the player, then it should work in Linux too. Those players are seen as external storage when you connect them.
Some other players require the use of special software to "convert" your mp3 file to some weird format (often, it's pretty much the same file but with a different header), or to transfer files to it.
I used the very simplest of mp3 players for quite a while, an USB-key with some buttons and a monochrome lcd on it. Worked like a charm, because as far as the computer is concerned it's just another USB-key. I only stopped using it because I got myself a telephone that also plays music. Bringing a separate mp3 player seemed a little redundant.