I think it's a neat idea. You'd likely be best off to focus your efforts on the inflatable back panel rather than the shoulder straps. The padding in shoulder straps weighs extremely little and I don't think there would be a weight or function improvement with inflatable ones besides flotation.
For the back panel, I would go pretty thick like 2-2.5" think so that it truly functions as a sleeping pad as well. The only downside of this is that you'd be moving the load further away from your back which would affect your center of gravity somewhat. Maybe there's a good compromise between performance as a pack and as a sleeping pad around the 1.5" thickness.
Typically the back panels of normal UL packs range from 10-13" wide and 25-35" tall. This is a bit of an usual shape for a sleeping pad. It would make a decent pad under your feet, but it wouldn't really suffice as your main sleeping pad. It would be extremely cool if you could figure out a way to make it larger (ie. torso sized) so that it could use it as your main sleeping pad. This would save weight, whereas using it under your feet would just add function but not really save weight.
This might be getting a bit crazy here…but one idea to make it larger is to have additional 1 or 2 inflatable sections (ie. wings) that somehow pull out of the side of the pack when you want to use it in sleeping pad mode. When hiking you'd just have the middle 11 x 25" compartment blown up, but then when you go to bed you could pull out the wings and inflate those (separate chambers) to get a pad 3x as wide…or 33×25". It would actually be easier to just have one large wing (~20" x 25") that pulls out of one side. To store the wing, it could just be rolled up to the edge of the back where as flap would fold over it and secure it with a few snaps.
On the negative side, sewing that would be pretty complex and a simple rucksack pack + torso sized sleeping pad would likely be lighter, less failure prone and good for times when you'd rather use a different sleeping pad. So it really depends on the value placed on the inflatable 'frame'.