Do I need to wait until the red "render bar" has gone completely from red to green before I click on "share" to create an .avi file? Thanks!
No, you do not.
However, doing so will help ensure that the first phase of your transcoding will go well and will help you identify any immediate problems.
As Steve points out, Rendering is first to allow smooth playback. Rendering can also be a test of how all aspects of the Project will likely perform together.