Yeah, if the app is never put into the foreground, we can't initiate a sync. Covering a use case like this would be possible, but we'd have to run a central server with access to information about your tasks, then use the push notification system to get the alerts to your phone.
(With the usual caveats - if you don't have a network connection, you wouldn't get the alert, for example, and the "central server" is going to be a privacy problem for some folks/tasks.)
We've got feature requests open on that, as well as the web service/interface that Avandelay mentioned; as always, email the
support ninjas and we can add you to those feature requests. Thanks!