The short answer is no. Some say there are emulators that will allow you to do so, such as Wine, but I've never had any success getting them to work with 100% success, primarily the ability to make purchases from iStore. If that isn't a concern for you, there are several Linux applications that will sync with your iPod and do everything that iTunes will, with the exception of buying music from Apple and playing Apple's DRM songs (which is quite easy to get around, if you're of a mind to do so.)
I use Amarok, which I have come to prefer over iTunes and there are others that work equally well, a simple google search will provide you with many choices to check out.
If it ain't broke, you aren't trying hard enough.