I rarely fall asleep while listening to anything, but I've long used some sort of recorded narrative to get back to sleep after I wake up in the middle of the night. Marie once asked me why, and I said, "I listen to semi-boring stuff. I think it takes my mind off racing thoughts or nagging worries, but I try to make sure the narrative isn't so interesting that it keeps me awake. It works really well." My go-to recordings: Benedict Groeschel and programs from Relevant Radio.
Well, it looks like my experience is shared by many others: "Anecdotal evidence from those who've tried to figure out why podcasts help induce sleep suggest that they're ideal for insomniacs who struggle with racing thoughts, anxiety, and over-active brains. . . [P]odcasts provide something to focus on that's engaging enough to quiet down your brain, but not engaging enough to keep you awake."
If you have troubles falling asleep, or getting back to sleep, you may want to try it.
You should, however, put it on a timer, so you're not listening to the podcast the rest of the evening. It will distract your sleep.
TWE, btw, is far too exciting for this use. A little TWE is like a little cocaine. That, at least, is what I hear in my dreams.