400W is recommended for that card, so technically the PSU is underpowered. What matters though is how many Amps it delivers on the 12v line; a 350W PSU doesn't deliver all of it's power on the 12v, but divides it over multiple lines. A 2000W PSU that only gives 2A on 12v will fail to power even the most basic system (extreme example, but you get the point).
No-name PSUs are never a good idea because the quality of current they deliver may be bad. A 12V line that actually carries 11.5V or 12.5V may well damage components and reduce the lifespan of the whole system. Because no-name PSUs usually are cheaper because they use cheap components, they are more inclined to have a reduced lifespan. Even if the quality falls within specifications when it is new, it might degrade over time and cause trouble down the road.
My brother had cheap PSU (also 350W). He upgraded from integrated graphics to add-in card (8600GT). 1 month later his HD started to go, month after that DVD-drive began malfunctioning, not to mention random problems he was having (crashes and freezes). Put in an Antec Earthwatts 380W (and replaced HD), not a spectacular PSU but quality. All problems solved and nothing popped up since then.
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Contritium praecedit superbia.
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