That pump is only rated for fluids up to 1.1 SG, so I kinda doubt it would be able to handle the whole grist, but I'm not really sure. I'd think you'd need something with huge inlets and outlets to prevent clogging. Sounds like an interesting concept though. Could you just use your lauter tun as the mash tun also?
I've been to some pretty large commercial breweries, and never seen a system like you describe, but I'd be very interested in seeing one or learning more about it. The large breweries I've been to often use a single heat source like a steam boiler, but still have three separate vessels.