No, in pHaestus' article, there's a power cable soldered to the inside of the PSU's power connector.
The diode is necessary, yes! Whenever you have a coil in a circuit, and there's power going through it, it will actually send out a surge, when the power supply is turned off. It's a switching effect. The diode prevents this current from passing through, into the PSU, and potentially damaging sensitive components, and that protection extends to all other components connected to the same power line (usually +12).
The key here is to select a relay that has good rated contacts, and draws minimal power for the coil. I found mine at
www.allelectronics.com , and mounted it all on a small PCB, then added standoffs, so that I can mount it nicely inside my case. I mounted a power outlet right on the same PCB, so the pump can simply plug into it.