As you noted, Nikon say Yes, the adapter is on sale at Amazon whose blurb says:
"The WU-1a is compatible with the following Nikon cameras: D7100, D5200, D3200, D3300, Df, COOLPIX A, COOLPIX P330, COOLPIX P520, COOLPIX P530, COOLPIX P7800, Nikon 1 S2"
therefore I think the answer is a cautious yes. The device is designed to be used with Nikon DSLR's whereas the Coolpix P520 is a Compact Digital Camera (according to Nikon) so there may be some limitations in it's functionality. Perhaps another member may have further information.