Carbon dioxide is produced as a metabolic waste product from exercise. Any sort of fat-burning you want to do is limited by the rate at which you can exhale CO2. This is why vigorous exercise is accompanied by heavy breathing. This includes not only cardiovascular training but also weight training. Lifting heavy weights will have you breathing very hard!
Unfortunately, if you don’t lift heavy (or if you use electrical stimulation that’s mild enough to sleep) then you’re not going to put your muscles into hypertrophy, so you won’t gain muscle mass either.
With respect to this idea, I'm not particularly interested in either of those goals. More the general longevity and health improvements that come with regular exercise irrespective of weight loss or muscle gain [1].
I haven't been able to find much in the way of research on the tolerability of EMS during sleep. I would be surprised if the idea is actually feasible. It just seems like it would be such a big win if it was.
Personally, I frequently toss and turn and breath heavily, and wake up with a high heart rate. But then, my sleep quality is terrible and when I got a sleep study the sleep phase diagram looked like a seismograph reading during a 4 hour long earthquake, so...
1: https://theconversation.com/exercise-extends-life-even-witho... (Maybe not a great source but I think there is a wealth of evidence for this)