^ I would consider a tiny 1.75" pipe all the way to the back of the vehicle with a big muffler at some point, severely restricted when compared to an open header.
The difference in just starting and continued running depends on how the carburetor is tuned. An unnoticed vac leak could result in a rich tune which could in turn make the truck run in the absence of a proper exhaust. Likewise, a lean tune with no leaks could cause it to stumble and stall when the pipe is removed.
In addition, restricting the exhaust at different points with various types of baffles and/or mufflers can change the back pressure to the point that it can alter the tq/hp characteristics of an engine.
