Check the amps on the +12V rail, then, since this is a generic, multiply by 0.75. Remember you'll be gaming for hours at a time, and if not an outright lie, a generic's rating may be at an unrealistic 25C temperature for a minute, not the more likely 40C continuous. As to performance, Dragon Age recommends a 3850; a 4670 is slightly better, so it should be fine at your stated resolutions.
Edit: to get rid of the smiley in the game's most common abbreviation.
The answer is a firm maybe. It all depends on your PSUs quality and as a generic unit it could end up being just fine or it could be underpowered and not work. No one here could possibly know. If you are going to give it a try a better choice would be the HD5750 if you can afford it. It's a better card and DX11 while using slightly less power.
For something slightly more likely to work with your PSU than the HD4770(and about 10% less powerful) there are the newer low power 9800GTs.
OK, 14 amps on the +12v rail isn't very good at all. I would stick to something that doesn't need a power connector like the HD4670 or a 9600GT or 9800GT. For the latter two make sure the one you buy one that doesn't have the connector. If you shop on newegg they always have pictures of the cards from multiple angles so the connector should be easy to spot if it's there.