Publicity photography with replacements: a question

The chandelier photo seems to show people in the audience so, in this case, it seems to have been at an actual performance though, if not, I suppose there could have been a small invited audience filling the first few rows of a full dress rehearsal.

It's called a Photocall which usually takes place in the afternoon (before an evening performance). This would be a separate event from the put-in (where like you said, not everyone would be in costume and scenes not involving the new actor could be skipped). The photocall is usually a pose and shoot type of event, usually without staging or music.
Equity wise, I'm not sure what the Broadway production contracts allow for a photocall on a long running show, but I would assume this is allowed (without having to pay the cast) when a new lead joins a show, or after a certain predetermined time passes. Maybe someone with knowledge of the Broadway agreement can tell us. All production crew and wardrobe/wigs would need to be paid however. I think Phantom can afford it!

In this particular case, the Phantom photos were indeed shot during a live performance by two photographers (Joan Marcus and Kyle Froman).