If the diode is in parallel, we have 2 possible cases.
1) Current is flowing through the relay coil in the proper direction(with respect to the diode, since the relay has no sense of direction), and the diode is basically not even connected.
2) Power is interrupted to the coil, yet it wants to get rid of its stored energy really quickly. In this case, the diode acts as a resistor(nearly a short circuit, actually), absorbing the load.
If the diode were in series, it would allow the relay to work properly. But when the power is turned off, I don't know what will happen. I'm guessing here, but my gut feeling is that it will PREVENT surges, instead of absorbing them. Which sounds great, but that energy still needs to go somewhere, and you're not letting it do that.
BTW, in case 1), if the diode is wired backwards, the relay will not engage, and you are basically faced with a short circuit scenario. The diode will not enjoy this.
However, I've used diodes as temperature sensors, and took a lighter to them when testing. At 200 degress celsius(internal temp of the diode), the diodes will still work. I'm sure you've heard that passing power through a diode will cause about a 1/2 volt loss. That loss is temperature dependant. At higher temperatures, the voltage drop becomes lower. That's right, diodes work better when they're hot.