This would add an extra bar. A pick up bar in music is not an extra bar, it is half of one bar, the other half is at the end. I know there was a way to add an actually pick up bar to the melody, but am now scratching my head!
What you are describing is how an anacrusis (pick up notes) works from a notational perspective.
From a performance perspective, all bars have will ultimately have the same number of beats with the exception of any lead-in notes played right at the beginning of the song.
The next time any pick up notes occur, they will be at the end of the bar prior to the start of a verse or chorus. That bar that contains these pick up notes will always have a full number of beats, though.
To answer your question fully, it's necessary to know whether you are using BIAB from a performance perspective or you are trying to notate a lead sheet.
Regards,
Noel