There is no question there is a labor savings to pour gypcrete and it is quite significant for this one building component. I have watched crews pour a complete floor in hours (wood floors in motels) and it is a cheaper trade because pretty much any laborer can do it since it is self levelling. You have a few laborers filling a pump (not much bigger than a grout pump) with gypsum somewhere at grade and a guy running around with a hose on the floor; whereas, you tend to see the same concrete trades and finishers when it comes to toppings (in our areas anyway). We've done up to four stories that way. I know we can make concrete self leveling too, but our trades always seem to cringe at the cost of super P. Short sited I know, but that is what I see the guys paying for the mud think.
Now is the cost savings of the gypcrete v. concrete topping significant on the basis of the overall project, that I doubt, but developers always disagree when they see the option that says they can save $x on the overall project.
This will come back to your comfort level. If your loads are that low and the spans are reasonable to avoid vibration problems without the added weight, I suspect you can make the numbers work just like Koot's example shows. I would bet you can drag your chord forces into the walls or concrete frames using a variety of connectors. Relying on the grout bond between the panels is the part where I would have the most difficulty. I suppose one could add a frame for redundancy, but then you are probably right back at the cost of a topping. I still do not like the serviceability aspect of gypcrete, but that is a discussion for you and your client. That discussion I suspect will be short unless they care about something other than cost. Be certain of your position before you go down that path.
Assuming your hollow cores are in the range of 24 - 40ft, I bet your pre-camber will be in the range of 0.5" - 1.25" when they are first delivered. Will the mech/elec trades be allowed to install their piping or conduit in the topping? That can be a good savings as well if the architect and timing permit. I would allow for something greater than 3/4" for the topping as well.
As for the footing cost savings, that is minor in the grande scheme of things. Unless you are minimum wall reinforcing levels, you could spend a bit more time detailing the wall reinforcement and you would save more on the basis of area alone. Now if you have problematic soils, I totally understand.