I'm not familiar with that cooler, but I'd say if it has a backplate you're ok leaving it on. (If you are moving your computer yourself, that is. I don't let anyone else move my electronics, personally.)
I haul my tower to my buddies 2hrs away every few months, and have now for nearly 10 yrs. In all that time only problems I have ever dealt with was AGP card seating issues. My current CPU cooler now is the TR 120 extreme, seen 2 boards, 4 procs and about 10 trips and not once has it ever caused me an issue.
But to be extra careful I marked my box so it sits board plane down so the cpu cooler is "not hanging" upside down in case, but rather the weight down upon the CPU. This ensure no undo stress is put on it.
If your careful and not going out in to the back logging roads, you should be fine.
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