No, you cannot power the PCI Express Development Kit, Stratix® II GX Edition from a power supply connected to a wall outlet and have it plugged into a PCI Express slot. You may only have the PCIe card powered by either an external power supply or the computer's PCI Express slot.
The board's on board regulators generate 3.3V and 12V from the external power supply and the PCI Express slot also provides these voltages. The two voltage sources cannot be provided concurrently to avoid contention.