If a task is visible to partners, the task will be included in e-mail notifications sent to the partners on that task, assuming that the partner’s profile is set to send e-mail notifications.
Based on your setting on the "Scheduling Settings" screen (accessible from the "Settings" tab on the main menu), CoConstruct will only make a task visible to a partner if it falls within a certain date range, if the task has no predecessors, or if the predecessors have "stable" dates. There are a number of factors to determine if a task's predecessor dates are stable, such as if the predecessor has been confirmed by its partners or if the task is already complete.
Even if a task is not visible to a partner, you can always click the "Notifications/Confirmations" link and force CoConstruct to send an individual work request anyway. That will make it visible going forward.
If you have given web access to your partners and have allowed them to see the full project schedule, then they will see all tasks when they view the full schedule. However, only those tasks marked as "visible to partners" will show on their personalized task reports, since those are the only tasks with stable dates.