Sorry, I responded earlier but I did not understand your question. I thought you were talking about charging them when the power is out. It looks like you are actually talking about them being dead during an actual emergency.
Obviously everyone’s usage is different, and maybe I have had a good experience because my loss is mild/moderate, but I can truly say that in the year that I have had rechargeable batteries, they have never gone dead. The only time they came close was when there was a problem with the firmware & connectivity and they almost ran out once, but since I had that fixed this is not an issue. I wear them for 16- 17 hours a day, and when I put them in the charger they still have usually 20-35 percent battery left. If the emergency happened right when I was going to bed that would be worse case, but I would still have time to figure out what was happening and get sorted, while grabbing my smart charger and charging them (possibly one at a time, depending on need) as soon as I could. It doesn’t take long to get a charge good for a couple of hours. If it happened during the night while I was asleep, my HAs would already be at least partly charged, giving power for at least a few hours, enough to figure out a time to charge them more fully.
If I contrast that to my last set which were battery powered, I did have several times where I forgot (or the batteries were weak) to break out new batteries before the other ones were dead and I didn’t have new ones convenient. One such time I was on a road trip and had new batteries in my luggage in the back of the car, but none on me. Another time I had intended to run out of the house quickly, and just forgot to grab extras.
Again, I understand that people’s experience may vary and I might be lucky. But I will add that I was hesitant about going to rechargeables, but decided to try them (I did have the option) and have found them to be much better than I expected and my nervousness about them turned out to be for nothing.