It will not hurt your torque converter.
I might use a resistor in your coil feed wire too.
You could also start your engine with the transmission in place (IN PARK) by making a loop of the cooler lines. The transmission could have several quarts of fluid put into it also as long as you have a yoke (safely wired) in the back of it but i probably wouldn't try topping it off like this (read as leave it two or three quarts low from a "capacity fill") since you would not moving and shifting a car, you are only assuring there is enough transmission fluid inside to lubricate things internally, probably a good idea if you intend to have an extended run of the engine with a radiator in place. (read as more than a few minutes). If you plan to run the engine for less than a few minutes, I would likely skip adding fluid since the assembly lube will be OK for only a few minute run. C4 transmissions are rather bulletproof like this.
Didn't think about the resistor, thanks for the reminder.
The C4 is still in pieces, which is why I was wondering about running the engine with the converter only, (and its attaching flex plate). I will be connecting a radiator and already have an oil pressure and water temperature gauge attached. The fuel source will be high enough to flood the fuel pump but remain below the carburetor level.
I still have to wait for the weather to cool a bit though...hot in Texas right now. Maybe by then, I'll have the transmission back together and either way, I still need to get an exhaust system for it.
Thanks for the help...Ray