Question about water pump tests

If the radiator hoses stiffen after the car is started, can it be assumed that the water pump is working and coolant is being pumped through the system? Or is that simply an indication that the system has pressurized?

While I'm curious about those signs in general, I'm also wondering if they're still valid for the vehicle in question: blown head gasket (and consequently exhaust fumes are bubbling the coolant overflow), no leakage from the water pump, and only the top radiator hose seems to get warm.

The water pump sucks from the lower hose, so it will be cooler than the upper hose. If it isn't, then you have a radiator or coolant flow problem.

A blown headgasket can cause the cooling system to pressurize very quickly, in a matter of seconds after you start the car. If you have exhaust smoking out of the rad then obviously you have blown a headgasket and need to replace it otherwise it will overheat no matter the cooling system.

So the water pump is working?

Usually you can look in the rad with the cap off and see coolant moving around, telling you that the water pump is working. With compression leaking into the cooling system from the head gasket, you will see movement no matter what.

The messy way.. You could pull the upper rad hose off, run the car and see if it poors coolant out. Make sure the thermostat is removed or open (HOT, will be dangerous).