External Power, internal daugher-board. Problem?

My good friend has a brand-new PCIe card that he intends on powering from an external power supply, rather than the power supply inside the computer chassis.

Both power supplies have an earth/ground pin - will there be any problems with this setup? Will things go horribly wrong with a puff of smoke?

SilverStone Strider Gold 1000W Power Supply http://www.silverstonetek.com/product.php?pid=285&area=en

Gigabye GTX 580 GPU http://www.gigabyte.com/products/product-page.aspx?pid=3684#ov

Mac Pro 2008 http://support.apple.com/kb/SP11