tl;dr: Yep, works like a champ. Best if you have big boxes (minimal gaps from the fold cuts and the edges.) As you say, Darth Bezos is a generous provider for this.
****************
Don’t use shiny cardboard, just the raw beige stuff. Corrugated is better (thicker.) Pull any staples, but don’t worry about the tape. It won’t rot, but it doesn’t hurt anything. If you do plant there later, you just pull out the loose tape as you encounter it.
After discovering the persistence of Bermuda grass (and crabgrass), I’ve started putting down an underlayment of contractors’ paper with generous overlap. This stuff or similar:
https://www.lowes.com/pd/Blue-Hawk-Builder-s-Paper-1-Pack-Paper-3-ft-x-140-ft-Drop-Cloth/50265367 Water it well, then cover with the cardboard, keeping the cardboard gaps away from the paper gaps as much as you can. Water the cardboard well, then spread a LOT of mulch, as close to 6” as you can stand (and afford.)
Weeds will still come up with time, but they are definitely weakened by having to work through so much, so they’re relatively easy to pull.
— if you do think that you may want to one day plant there, you can put a layer of compost between the contractor paper and cardboard. Not necessary, but it will help future fertility and tilth, and earthworms will be in heaven.
I’ve built at least 8 garden beds this way. No tilling, minimal weeding, rich, moisture-holding soil. Great stuff. And obviously, it’s just as effective for mulching alone.
Landscape fabric is evil. Kills the soil underneath (soil is a living organism), and a freaking nightmare to remove later on.