You might be able to remove the water pump without removing the radiator, but it would be hard.
You will definitely need to drain the system, it's going to happen anyways when you remove the pump. There's a little drain petcock on the passenger side of the radiator on the bottom, unscrew that and the coolant will drain. Once the coolant is out, it's not hard at all to remove the radiator, just the two big hoses, one little hose, two bolts at the top and it lifts out. I would do it if I was going to replace the pump. That will free up the few inches in front of the motor to make it much easier to get the bolts out. The biggest obstacle may be removing the fan clutch, mine was seized on the pump, and didn't come off (replaced the fan and fan clutch too, so it didn't matter).
For the fan clutch there is special wrenches you will need, they can be gotten through the loan-a-tool at autozone or the like.
It is definitely advisable to drain the coolant not just so you don't lose it when you remove the pump, but because it likely needs replaced anyways, especially if the water pump went bad.