If you had 4 dual GPU cards in one system, enough CPU threads to feed them and some magical way to cool them, could you theoretically make this happen on this project?

In theory, yes. In practice, it's not presently feasible (for here).
While there might be issues running 8 GPU's (boards, case, PSU, cooling), especially on some OS's & while 7 might be more practicable, in theory up to ~16 GPU's are possible, but that's not the real issue. The last dual 'GeForce' GPU of note was a GeForce GTX Titan Z (GK110) [375W], from the GeForce 700 series. As the 1080 can theoretically do as much SP work using 180W, you're not likely to opt for a two generation old GK110 for this project. Other issues include high-end/high-cost system requirements and there are multi-GPU scaling issues. Even with 40 PCIE lanes, high end systems struggle to support 4 high end GPU's.
There isn't a dual Quadro or Tesla Pascal and for a dual socket Xeon that could support 8 GPU's you would be getting into the tens of thousands of dollars anyway.
In a few months time all this might change. High end systems will hopefully better support high end discrete GPU's and we might see additions to the Pascal range; a dual Pascal @ 300 to 375W TDP looks very doable to me and would make a lot of sense, albeit with a dollop of wishful thinking. In reality it would be at least as likely to arrive in a Titan as a GF, and neither could turn up. However, we saw app scaling issues with the 980 and it's blatantly there with the 1080, so a single GPU 1080Ti probably wouldn't scale at all well for here so a dual GPU option would make a lot more sense for the app and in terms of performance/Watt (which is alas more important to crunchers than gamers).

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