Tony,
All cooling systems run at pressure when warm...they do this for a reason (water boiling point increases when it is under pressure. For example instead of boiling at 100 degrees it will boil at 120 degrees under a certain pressure).
Yes the temp will go up enough to put the guage into the red if the fans do not work. If you ignore it and left it idling then eventually it will get hot enough for the piston to expand in the bore and seize. When a vehicle is left stationary while running the cooling fans are the ONLY thing that stop it from over heating (this statement excludes diesels where the heater will actually cool a diesel down as they run a lot cooler than petrols). What stops the car from over heating when moving is the air flow through the front of the car. The fans are not used at all while the vehicle is moving unless it's moving at low speed.
If your car over heates while traveling then you have a problem. The car will WANT to over heat when it's stationary (as if sat in traffic) because it doesn't have the air flow through the radiator to keep it cool which is where your cooling fans come in.
If it is building up an excess of pressure then you have a head gasket problem. To check this you need to run the car from cold with a cooling systems pressure tester connected with no pressure on the guage to the header tank. watch the guage as the car gets warm. It should rise and hold around 10 psi of pressure gradually as the engine warms up. This will rise slightly when you rev the engine up and drop back when you let it idle. If when you start it from cold, it rises rapidly, or it suddenly starts to rise rapidly and doesn't stop rising (you will have a danger marking on the pressure tester guage..usually a red band from 15 psi upwards) and goes into the danger band then you have a head gasket problem.
Another thing is I have known the header tank cap on 2wd Cossies to become weak and not let the cooling system to build up to it's normal operating pressure so get a new one of them.....
You need to find out if the car over heats or gets up towrds the red while driving at a steady speed of say around 40mph. If it does then you have a problem and I would repalce that water pump AND header tank cap.
Let me know how you get on.