The cargo hold of passenger aircraft is pressurized to the same level as of cabin. The atmospheric pressure at sea level is 14.7 PSI. The minimum allowed pressure is 10.9 PSI (8000ft equivalent), which is about 3.8 PSI difference. It is comfortable enough to breathe for you. It should not cause the well sealed liquid cooler to leak/burst. Unless a rapid depressurization happens, which is very rare.

Being said that, your biggest challenge is how the cargo is handled. Even with fragile stickers, the probability that your packed bag thrown and all is really high. Damaged caused by that is much more destructive to the cabin and liquid cooler. So, if you really want no damage, pack it well so that it won't get damaged while being thrown around.

The cargo hold of passenger aircraft is pressurized to the same level as of cabin. The atmospheric pressure at sea level is 14.7 PSI. The minimum allowed pressure is 10.9 PSI (8000ft equivalent), which is about 3.8 PSI difference. It is comfortable enough to breathe for you. It should not cause the well sealed liquid cooler to leak/burst. Unless a rapid depressurization happens, which is very rare.

Being said that, your biggest challenge is how the cargo is handled. Even with fragile stickers, the probability that your packed bag thrown and all is really high. Damaged caused by that is much more destructive to the cabin and liquid cooler. So, if you really want no damage, pack it well so that it won't get damaged while being thrown around.

Note: Those coolers are regularly transported using airplanes by manufactures and distributors.