If you have them snug enough so nothing moves but not too tight it won't harm anything, unless you're doing something really jarring like off-roading. Just make sure you use pads between the cooler and whatever it is you're mounting it to. I've had one on for over 15 years and nothing happened, and it does help increase the life of the transmission. I'm not sure of the exact numbers but every 10 to 20 degrees drop in oil temperature will increase your trans life by so many thousands of miles....something like that. You'll be surprised how hot that sucker gets in the summer or after you've climbed a steep grade.
Yeah I thought about what effect it would have, I think the effect of the zip ties on the radiator would be minimal. Its secured on there pretty tightly and the pads were used.
Think the figure was every 20 degree drop in temp doubles the life of the transmission. I installed a fairly big cooler (15" 1/2 x 7 1/2 x 3/4"; 'heavy duty' flavor) so I should be good.
Finally, my transmission will be protected from my rev-happy driving style.