I assume you mean an iPod Mini's Firewire charger. Yes, it should work. I charged mine all last night with the Firewire charger from a 3G iPod. However, you can only sync over USB..
Apple used to make a split Firewire/USB cable that MIGHT work...you'd have to plug the Firewire into the wall and the USB into the computer. However, it's pretty old and I'm fairly sure it's been discontinued....Probably difficult to find today...