Are refrigerators watertight?

Just wondering:  You can find free deceased refrigerators all the time... if you tipped one on its back and took the doors off, could you use it as an aquaponics tank?

Yes!
I have one that I used as a worm bin, it holds water quite well.
It will probably become an azolla growing container.
My green house in progress has two waiting to be converted to sub irrigated planters.
Defunct chest freezers are deeper, if that makes a difference for your purpose.
The only issue I have is the refrigerant that is usually still in the compressor of an old freezer/fridge.
I don't have the means to recover it, and I don't want to vent it.
This limits which derelict devices I'm willing to take and use.

The refrigerators I've seen have cooling vents at the back, so they would not be watertight.

Chest freezers will hold water.

It's been a while since I did my conversion, but I did use concrete in one part of it.
I think it's maybe 3" thick at most.
Here's the bottom of the freezer section, where I used the concrete:

https://permies.com/t/134669/a/104966/IMG_20200411_122118.jpg

Here it is months later,  still holding water :

https://permies.com/t/147534/a/117241/IMG_20200907_144258.jpg

William Bronson wrote:It's been a while since I did my conversion, but I did use concrete in one part of it.
I think it's maybe 3" thick at most.

That makes sense. I think it would work just fine.