Hi,
There are a lot of somewhat similar, low thermal mass, poly sunspace/greenhouse designs around and in use. They can be quite effective as solar heaters -- lots of collection area for not much money. So, I don't see why that scheme would not work.
Some people find that some form of insulating material (e.g. garden bark) under the black poly on the floor keeps the heat from going into the floor.
The replacement thermal controls that HD and like sell for controlling attic fans make pretty good controllers for this type of heater. Its just a thermal snap switch with an adjustable turn on temp of about 85F to 120F -- just set it to turn the blower on at the temp you want.
Can you provide a link or source that shows the design in more detail?
One potential problem might be snow accumulation on the deflated bag?
Or, how it behaves in the wind (but some inflatables do quite well).
While the idea of the inflatable/collapsible structure is clever, I'm not sure that one of the inexpensive pipe frame greenhouse plans might not be better in the long run?
Lots of them here:
http://www.builditsolar.com/Projects/Sunspace/sunspaces.htm#Greenhouse%20Plans
The main thing if you want it for house heating is to keep the thermal mass in the GH itself very low -- this way it heats fast and is ready to transfer heat to the house very quickly after the sun gets on it.
Gary