I know for certain that my Archos 604 WiFi will resume after file transfers, but I do not use syncing because it would require me to use WMP as a media manager. So I just use the player as a mass storage device, which is my preferred method anyway. Still, after every connection to the PC, the player has to update its library. Even after that, I can always resume my track (there's a dedicated resume button in the main menu). I can resume video files as well.

I use it for listening to podcasts in the car as well, and what you're saying is also important to me.

I can only speak for the 604 WiFi here, which is last-gen hardware and software. The current model is the 605. However, I wouldn't be surprised if this is the kind of thing that carried through to their other products, and you'd probably be able to ask on the forums if you wanted to find out.