Sharing my experience with bad coolant temp sensor (CTS) on my 95 LT1 -
My CTS failed low (constant, not intermittent), but not failed to the point that a code was set.
Flooded out the engine - wouldn't run when warm. Could start it with flood clearing mode (throttle to floor, no fuel) but would flood out after running a few seconds. Pulled the CTS connector to cause a hard failure. Started and ran well enough with code set and no CTS to get me home.

Testing without the sensor in play (and thus wiring as well) may help narrow things down.
Note my experience was with LT1, so others can chime in on any differences to your application.

Hope this helps -
Jim