The short answer is NO.
I have called Bytecc, DLink, Silverstone, StarTech and others to confirm this is the case even on new PCIe 3.0 slots which provide 300 Watts of power. Most server slots are PCIe 2 which provide 75Watts and it is just not enough for USB 3 even if your external USB3 drive has its own power.
I have also tried several techniques over the last year and done much research but only found found:
The Molex does route +5V and +12V lines to the add-in card. So even though hard drives connected to it have their own power source, the add-in card might not be stable or even work at all.
Typically my issue is that I want to add a USB3 card into a server which has NO molex power connectors. Often I see servers with only power to the motherboard, backplane and to the CPU (i.e. no traditional 4 pin Molex or even a single SATA power). This is frustrating.
If you want to bang your head further, take a look at: