He just said that most of the code, and usually all of it, will be the same. Only very few things are OS specific. Just run it on the linux machine and see if it works, that's the easiest thing
What I mean by saying most things are *nix only and not windows only was that you'd more then likely have more trouble switching from a *nix environment to a windows environment. Since your vica-versa, then you should have vitually no problems.