If I had called, they probably would've said no. The admitting officer was very hesitant in letting all (two adults and two children with one interview slot) of us in, but he eventually relented and passed us off to a much nicer officer. Done in 16 minutes.

As I said in the walk-in thread, bringing an extra person (significant other or child) probably won't cause much grief. Any more, and don't be surprised if they say no.