@marinelife is correct about the baby pressing on your vein that returns blood from your lower body. It can also press on the artery that supplies blood to your kidneys, the baby, and your lower body. If the blood supply to the kidneys is cut off for an extended period, it could cause problems with your blood pressure. It would take quite a while and quite a bit of pressure for this to cause serious damage though.
With that said, waking up on your back isn’t really that big of a deal because your body is going to do what it needs to do to support the baby. By the time you would do any damage from having the baby interrupting your blood supply, you would most likely wake up from being uncomfortable anyway. If you wake up laying on your back, you want to lay on your left side for a bit before getting up if you can, as that is the best position for blood flow.
I personally can’t sleep with any of the body pillows or pregnancy pillows that they have out these days. I go to sleep on my sides and if I wake up on my back, I just turn to the side. I wake up on my back all the time because laying on my sides causes a ton of pain in my shoulders and hips (due to the loosened ligaments thanks to the shift in hormones).