You are correct; there is a way to turn off notifications for a group, but a member would have to set it that way, as it doesn’t default to that. It is just a heck of a lot easier to post a pre-event announcement on the group wall then to send out a mass e-mail.
As for sending out a mass e-mail, FB limits the number of people on it to 20. See Help Link – ‘How many people can I message at once?’ Notice that it also mentions that if a group member is not on your Friend list, they will have to be notified individually. For example, we now have 85 members in our high school class group. Not all of them are on my Friends list. In order to send everyone a message, I would have to make a list of all members, figure out which are on my Friends list, send the same e-mail 20 people at a time, and then send the notification to the others individually. Yuck.
As for an event request, once you have the date, it will show up in their Events alert folder, whether they are on your Friends list or not.