No.
The Mark VIII pulls over 100 amps for milliseconds during ramp up. That little relay will shoot poo all over itself in a short amount of time (and inductance will wipe out the Normally Open contact anyhow).
For the easy way to do it (and a real nice way in hot Texas), use a DcControl unit. Other guys (Urban for one) have had good luck with the SPAL controller. FAL also makes a decent controller but I'm not sure it can handle the Mark VIII.
If you really want to do this using your own relays, At a minimum, I would get a Bosch 75 amp relay for high, and use the factory input to the HEDF relay for your new fan. Even better is to get two 75 amp relays and do this for both low and high. The will be controlled like stock but use HD relays instead. This will last a lot longer. Of course, by the time you buy two 75 amp relays, you're well on the way to a quality controller (though with the SPAL and maybe FAL, you still need a high speed relay IIRC. With DcControl, you do not).
No matter what relay you use, the flyback diode is a good idea.
Random thoughts.
Good luck.