It should. It may be a bit hard on it, but the system should not need more than the power supply label lists(remember older power supplies start to loose some capacity so I would keep an eye on it.).
It is actually multi rail, but that is not an issue as such.
Lower powered cards may be a better long term bet(even a 5770 should take less and be faster), but for a second hand system, you work with what you have.