Wouldn't I only need to connect it if I wanted to transfer funds from the wallet? I mean if the wallet's not connected the funds won't show up, but the addresses in it will still be connected to the btcn right? that's what I'm concerned about.
You've got it right. Here are a few related threads confirming it :
http://forum.bitcoin.org/index.php?topic=17697.0 https://forum.bitcoin.org/index.php?topic=16845.0Really easy to check your balance, just go to the main blockexplorer page and put one of the addresses you've generated into it. It will look up all transactions related to that account. Try it with your current wallet.