I am guessing that the network provides some sort of catch-up mechanism, but I would be interested to understand better how a given wallet after of period of offline activity gets updated to its latest BTC value.
Yes, once your client is online and has a few connections, the catch-up mechanism that it will automatically start downloading all the latest blocks (it gets the block chain up-to-date). Once you're up-to-date block-wise, you'll see any transactions that occurred while the client was offline.