Monitor paper wallet balance without importing private key? I generated a paper wallet offline and running from fresh OS, and I'm not going to ever type that private key into a computer until it's time to spend the coins.

But I will send coins to this address as a 'piggy bank'

My question: can the Qt client be configured to track an address and update the available balance for an address, without the private key ever being entered?
Try using BlockChain.info - you can add a watch only address and then receive email or SMS alerts every time it does anything - so you don't even have to consciously keep an eye on it. 

Edit: I apologise, I didn't see that you wanted to use QT for it. I don't know of any way to do this, so propose blockchain as an alternative.