No-one is worried about the effect of the water/chlorine/fluids are gonna have on the tranny cooler, they're concerned with the effects aluminum, stainless, and possibly and residual fluids are gonna have on his clones... I'd also be worried... Copper will leach in a res full of nutes which is why copper wort chillers aren't used, stainless is the choice for those but I've "heard" aluminum will do the same so... but if the coils/tubing are stainless I'd think about it but the residual oils is where I'd stop and find a different solution to the problem... If you were gonna "dip" the cooler into your res and run chilled water in a closed loop, I'd say go for it seeing it's easier to clean the outside of the tranny cooler.... But running your res water through anything with any kind of oils aside from hemp or hash oil (just a pun, not serious)....I don't care how good u clean it, it's still a liability... And it's most likely not gonna just fuck up a batch of clones, it's gonna coat the inside of your cloner with the same shit possibly permanently, so again....I'd also be worried...
And for what it's worth... a water temp of 73 degrees for aero cloning is mint, basically anything below 75 is primo... I run mine with no additional cooling at all and it ends up in the 80's most times in the hotter months... Roots in 7, plantable in 10-12 days usually... 60 site Ez cloner, filled with municipal tap water, 15 ml of protekt silica, 3-4tbs of hydrogen peroxide... Add those run it for 24 hours, add clones...smoke joint... Ive never checked ph....never checked ppms.
The plants can't eat anything due to not having roots so checking all that is wasted energy until they have roots and even then it's really not a concern because you don't want feeding/growth, you want root growth and only root growth... The added silica is to help with transpiration but honestly I add what I add and don't come back for 5 days other than a peek here and there to make sure a timer hasn't malfunctioned or something... Water level is my only concern aside from the afore mentioned... As long as u keep the RH and room temp normal-ish you won't have any issues... If your room temps and more importantly your humidity....are higher than they should be; by all means seek additional cooling for your cloner, but it would serve you better to get the room temp and humidity in check...
Also the thing generating the heat in your cloner is the pump, you can run a timer on 15 on/15off up to 30on/30 off...helps keep the res cooler by the pump not running 24/7... Supposedly it speeds rooting as well...? A suggestion by one of the builders of the ez cloner... I recently did the 15/15 and it work as advertised... Didn't really notice a difference in rooting times but they looked all perky n normal beginning to end... But initial start up is what kills most electrical things like pumps so take that into consideration...
One more thing as if I haven't said enough, cooling with air is way less efficient than with water... A chiller like the above mentioned diy dehumidifier and stainless wort chillers would be a better investment... Especially if u have other resivoirs that need cooling...