The power supply fortressd listed above is not a recognized name brand. If you were to purchase a power supply your best low cost option would probably be a Corsair 400cx ($39 after MIR on newegg)--I own it, works great. Other good power supply brands are Antec, OCZ, Seasonic.
Back to your original question... yes it should work--but no it its not recommended. An upgraded power supply will make your system cooler, quieter, more power efficient, and less likely to burn up.
This power-use graph gives you an interesting perspective between cards in this range.