Once you've bootstrapped/integrated with the network, it takes a minute or two for a new update to reach you in my testing. The initial time to bootstrap onto the network is around five minutes.
The traffic consumption is pretty high, because it becomes a full peer on the I2P network. Over a month I would expect it to consume around 1GB or more. If this becomes an issue for people, I may add the ability to be a non-contributing peer.