I have had this predicament several times. I don't like the idea of using a rusted/flake filled radiator. It seems like it just keeps putting more crap into motor. I would not use it until I was sure it's clean. Either by rodding, flushing or buy new.
You can, of course, fill a motor with water and run it for a few minutes without worry, no radiator.
Recently I ran a motor on just a garden hose by using large PVC sized to rad hose ID. Clamped rad hose on. Adapted large PVC down to a female garden hose connector. This way you have good water pressure into motor. Ran the output into a container so I could see and examine the rust and such. You can do this both ways to get a back flush if you want. PVC will have to be different OD's. 1.5" and 1.75" usually.
I think I ran with T-stat out.
Yes JW, just to see how a motor runs, a leaking water pump would have been OK.
