Driving with a broken serpentine belt for only one mile on a rough trail will seriously overheat the engine and damage heads/head gaskets beyond repair (in the first place). Think you can cool the engine down by only turning it off every two minutes? Fine. But without a belt, the alternator won't operate either. And no alternator = no battery recharging. Your strategy might work 20 or 30 times (depending on the quality and condition of your battery), but you won't go very far before getting stuck for good. Probably not more than 10 miles / 16 km (and I'm optimistic). For that reason, no Jeeper should drive long distances in the wilderness without carrying a (working) spare serpentine belt at all times.
4 things to know
1. First, there are a lot of jokers on eBay or ignorant resellers on other platforms who don't know a damn thing about what they are selling to Wrangler JK owners. They just copy/paste the same descriptions/fitments again and again. When you realize it doesn't fit, the 30-day or 90-day return policy has often expired.
2. Second, I think you should avoid budget serpentine belts with weird names (made in China) that pretend to be OEM. I know many Jeep owners (including myself) who went that route and it's a nightmare. Too long, too short, too narrow, too large, doesn't fit on the tensionner, or just slips.
3. Third, I'm 99% sure that you won't remove the current serpentine belt to just test the new one. It's a lot of work after all. So, before you start your journey, you better buy the right product and be 100% sure it will fit.
4. Fourth, many reputed stores on the Jeep scene are confusing everyone with the mention "with air conditioner" and "without air conditioner". Well, I figure you already know if your Wrangler JK has air conditioning or not. But if you don't have A/C, the trick is that there is an idler pulley in place of the a/c pulley (also called an Air Conditioning Bypass). Just verify and make sure that the nobody removed that pulley before you. So, if it's still there, you can use a full-length belt like anyone else.
A/C Idler Pulley