Windows has a default driver, which means you can copy photos from the iPhone without using iTunes/iPhoto.
But you certainly can't access the rest of the file system without jailbreaking the phone. There used to be apps that allowed this, but Apple killed them.
Sync Your iPhone Wirelessly in Linux
Apple may open up its iPhone and iPod touch devices to third-party apps next month, but the chances that Linux users will get invited to the party are slim at best. That hasn't stopped some intrepid hackers from coming up with a better music-syncing solution than the one Mac and Windows users have--a two-way wireless transfer, from almost any music organizing app you like, no wait for iTunes or USB cable required. Linux users, let's take a look at how to set up your iPhone or iPod touch for any-time wireless access after the jump