You can safely assume it can't support your GPU. Most factory desktop PCs have around 300W, some even 250W. They are unreliable for any adding of extra components besides some RAM or HDD. They are as cheap as they get to keep the overall costs low.
Plus they never include a 6 pin connector, which you would need. It's possible to use a 6 pin to molex cable if the PSU has spare molex, but it would also need 400W plus 20A on the 12V, which you won't find on a factory desktop unless it has a dedicated GPU already.