There is a notifications profile on BlackBerry that is not visible by default but can easily be turned on that does exactly that- it's called "All Alerts Off" - WAY more silent than the "silent" profile which still blinks the little red light and pops up calendar alerts.

I have seen similar notifications profiles on other mobile OS as well, perhaps called "Do Not Disturb." In any case it would be a good one to create yourself and have.