Send email notifications only when offline

It would be great if there was a user option to only receive email notifications when they're offline, or to get a summary email of the notifications that they've missed if they don't visit the site for some period of time (as Stack Overflow does).

There's no point getting email notifications when you're actively browsing the site, but equally if you're only an infrequent visitor you don't want to miss any replies to things that you're interested in or that you posted, and something like this would strike that balance (while also helping to boost retention in a user-friendly way).