I have a noname 1200W PSU 80bronze and 3 290X (one with Powered Riser) and the System uses 1120W in total. The cards doing fine with 885kh/s at 60grad celsius.
When starting up the system uses 150W.
So I think it should work.
I agree, the manufacturers are conservative with the spec (which is good).
I run MSI R9 280X, which is specified for 375W on 12V.
With default volting it draws 300W on the 12V at full hashing, with undervolting its 270W.
One more comment; bronze rated PSU has typical less efficiency at full load, as little as 80 % efficiency, maybe that is worth taking into consideration if you pay for your own electricity. That is 200W wasted, unless you use your rig to heat the house