Forget about those flimsy little stackable storage crates you get from the home DIY stores. They're thin walled, I wouldn't trust their longevity, plus they're too small anyway to even make it a worthwhile project.
But if you went the industrial route, ie big old thick walled heavy duty totes then it can be done, I've seen a few threads over the years on here.
The main problem you have, as mentioned, is silicones inability to adhere to plastic. But you'd get round this by using the silicon as a gasket only. The structural integrity of the viewing panel would come from actually bolting it to the actual crate/tote/box, whatever you want to call it.
At work we have all manor of large totes coming and going regularly. Heavy duty with thick walls so bowing is of little concern. I've toyed with the idea in the past of doing something with them, but never got round to it. You can pick these type of totes up on line from salvage places and such.
Below is an example of one of the many types of totes we get in. As you can see they also make great paddling pools for when there's a heatwave, lol.
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