Easily. I have one running on a Dell 275W PSU with a smaller +12V rail than your PSU has. There is a GTX 1050 soon to be released that has no 6-pin header. Not sure how long before we see it here in the US.
http://wccftech.com/asuss-latest-geforce-gtx-950-graphics-card-requires-6pin-connector-features-1228-mhz-boost-clocks/