Well - we won't know without trying. But it's clear that in the Read/Write Web Facebook case, a bunch of people had thought that they had logged in to Facebook when in fact they hadn't. And that they didn't even know where they were.
You may not want it every time. But at the moment, we don't even have it at all. That's restrictive in the kind of messages we can send out.
For emails flying off the screen: the execution is in the detail. A few seconds may be too long. For some people, it may not even be long enough. But the animation isn't necessarily just showing that an email is being sent: it can convey a lot of other information in a clear, yet subtle way. It's interesting that there's no visual cue when an email is sent that distinguishes between sending to a single individual or a group of people, or an even larger group of people.