Hey!
It's interesting, because being overweight/obese is one of the main causes of sleep apnea--and then the sleep apnea makes one more stressed. Stress, in this case from lack of sleep, can cause the body to hold on to fat. I'm not a doctor--this is just what I've heard.
People do have an easier time losing if they are getting enough sleep/rest. This is only my impression, however--I don't know whether any studies have been done.
The cost of the apparatus is kind of high, I think, and the question is whether you'll find it comfortable enough to sleep--but you might want to give it a try if you're offered a free period.
I'd say, don't expect to "sleep away the pounds" without also limiting your intake. But hopefully, some other members with more experience will post and give you more information.
Losing weight WILL help the problem.
Jay