It it were a high quality 350W PSU then it would be enough, but there are very few quality 350W PSU, most being rated higher wattage than that, and it's almost certainly a piece of junk because it's bundled with a case and also the lack of major branding, although some might feel Foxconn is a major brand yet they make a large % of the lowest end junk PSU that are bundled with cases.
So the answer is no, I wouldn't use the included PSU with ANY build, let alone one with the extra load of a video card instead of using integrated video. Often I wish they'd just knock $5 off the price to be able to get the same case(s) without those junk paperweight PSUs.