Can I check balance of wallet.dat without downloading the block chain? I have bitcoin associated with a wallet that I am now moving from a server to external storage for backup. As far as I know, all I need to do is copy the wallet.dat file to external storage and I'm good (given that I won't be doing any transactions in the foreseeable future).

My question is: once I move the wallet.dat file over, how do I check --without downloading the block chain -- the balance associated with it to make sure all is well?
I think your question has an underlying misconception. The wallet only contains bitcoins in an abstract sense: In realitas the wallet only stores the private keys that enable you to spend the bitcoin balance that is associated with your addresses. Think of it this way: When you look into your wallet, you only see a number of little boxes. You know that all these boxes are yours, but from the outside all boxes look the same, regardless of what they contain. You can only know how much you have in this boxes, by opening each of the and counting their contents. This "looking into the boxes" step happens by looking up the balances of your addresses in the public ledger (the block chain). The wallet.dat might contain the balance that was last counted when you compared to the blockchain, but can only be updated to the current state when counting the contents of the little boxes again.

So, without downloading the blockchain and having your software calculate your current balance, you could only check "if everything is alright" by looking up specific addresses. If you received your bitcoins in one transaction the balance is associated only with one address and this address could easily be written down or memorized separately from the wallet. You could then proceed to look up the balance of it on a website such as for example http://blockchain.info. This can be done safely, as the address alone does not allow anyone to spend the bitcoins.

So, summing up: Just from the wallet.dat you cannot get an update on the balance without acquiring additional information. You can however check the balance of addresses directly by using publicly available information.