Will -
If the waterpump is leaking say overnight and the coolant is dripping on the drive belts this could cause them to slip and squeal at start-up. Waterpump seal squealing typically only takes place with the cooling system at operating temperature. If your waterpump is leaking you will loose some coolant from your system and typically see some leakage tracking down the front of the pump from the drainhole provided for such leakage, perhaps onto the floor. If the pump is leaking, pump failure isn't far away. Unfortunately GM waterpumps like that on your Corvette often fail before 50,000 miles. Incidently, if the drive belt for your power steering pump slips bad enough due to such leakage you can loose all power steering assistance; this happened on a Cadillac of mine at only 30,000 miles and I was entering a curve onto a bridge and nearly lost control and would have gone off the bridge, so be carefull.
Jack