Computer PCIE slot power in parallel with external power supply?
Yes and No, think about it for a minute. Lets say that your PC supply is exactly equal to the voltage of the external supply. Unless the PCI card has separate Vcc's you are effectively connecting the PC supply to the external supply, if the voltages are exactly the same, then no current will flow between the supplies an you'll be fine and you can parallel the supplies. This works in an ideal case.
(You also need to connect the grounds together.) 

However, in the real world the supplies are not equal, source resistance (including cable resistance) will create an imbalance in voltages. Lets say one is 5.05V and the other is 5.15V. You'll get current transfer between the supplies based on the resistance between them. If the cables and source resistance is under an 1/10 ohm (which isn't unreasonable) then you'll have 0.1V/0.1Ω = 1A (as an example) and one power supply will be dissipating power in the other and that is bad. 

So the answer is no, unless you have some way to match the voltage exactly (if you had an external control pin to regulate the voltage or the supply had some kind of control loop then this would work) OR if the Vcc's are seperated then the answer is yes.