|The short answer is that in some systems you can get it to work and other will not.|
When you power it down and move the drive to the add on card boot to bios and see if the drive shows. It may or may not, hopefully it shows under hard drive choice. Also having an option to boot from choices may help. Even a pci-express boot option may have to be selected. I suspect that the boot order needs to be edited each time you swap between internal and pci-e.
I doubt all of this will speed up your system.
A Pit Bull is like a gun you can pet. And there is no safety on it.