Why are you considering cleaning the cooling system? I've been inside 20 year old Duramax 6600 engines and didn't see any cooling system problems... In fact, the 20 year old Dex-Cool orange coolant still looked pristine and I didn't see any corrosion on the aluminum or cast-iron parts - none. I didn't see a need to service the cooling system.

Yes, you could run the engine without the t-stats. However, the engine won't reach operating temperature very often (in the winter).

I tried running Lil Red with its coolant surge tank cap loose... back when its head gaskets were causing a cooling system over-pressure problem. A loose cap caused coolant to leak badly over the inner fender. So, I didn't do that again.