As soon as your client broadcast the transaction to the network, you can close your client. I don't think there is any indication in the gui, but after you've made the transaction you could check http://bitcoincharts.com/bitcoin/
and if it's there, you can close it down
If you double-click the transaction, it'll say "X confirmations, broadcast through Y nodes". If it's more than 4, you're probably good. If it makes it to bitcoincharts, then it's as good as confirmed.