1997 Audi A4 engine over heating

Water pumps generally fail in three ways, they leak, they seize, and they fall apart.

Leaking is easy, you will loose coolant, as your pump is next to the timing belt there will be a burning smell, though most importantly it will leak and you will loose coolant.

Seizing is easy to spot as it generally damages things around it, belts, hoses, loud nasty squealing sounds, this is seizing.

By falling apart I mean internally, such as the impeller falling off the drive shaft, or bearing giving out and causing grinding and leaking.

If your pump isn't doing one of these things I would get a second opinion on what should be done as there are so many things in a cooling system that can cause over heating, thermostat, radiator cap, bad hoses, head gasket, water pump, and on and on.