We just sent out an email blast using Mailchimp and a number of people unsubscribed from our list (via Mailchimp). How long will it take for their unsubscribed status to appear in LGL?

Updates such as Mailchimp subscription status flow into Little Green Light nightly. They will appear in your integration queue and then you can save them, which will cause the Mailchimp status in the constituent record to be updated in LGL.

Even if you don't save the updates from your integration queue, however, there's not much harm. The only impact it has is that it looks like you have a few more subscribers in LGL than you do.