Yes. This is a quote from the Pandigital 'Getting Started' guide. "You can also charge the battery using the USB cable connected to a powered-on computer or a USB power adapter when the device is off or in sleep mode." I sometimes charge my Supernova with a generic Mini-USB charger and have found it is a v-e-r-y slow trickle charge. It takes 8-12 hours to recharge fully with the unit powered down. In sleep mode it takes even longer. Your best bet is a proper charger. Pandigital ships it with a generic power adapter made by DVE. Google DSA-12PFA-05 (the DVE part number) and you will find lots of sources, as well as the specs if you want to try to find a substitute.
Not in a conventional way, no. You can try the online buy/sell/exchange sites besides amazon/ebay for the charger where you have a very good chance of getting a charger in a lot cheaper price. Or ask an electronics expert to customize a charger for the gadget if u won't get one. But that might cost you a bit too much. Good luck hunting though.