If its a quality 350W it should be fine. Even with an overclocked AMD chip you wouldnt be drawing more than 200W through the 12v.
However, if its a generic unit and/or 3+yrs old, wouldnt trust it to hold a graphics card.
From the little I can find of it online, that PSU looks pretty generic.
See i would buy a new psu but i don't know if it would fit in the case any help?