If you have cellular data turned on for iCloud photos then it will do limited syncing over cellular data, but if there are a lot of photos to sync it will wait until you connect to wifi. It may require wifi for the initial sync, though. It also will normally sync under battery power, until the battery drops to around 20%, at which point it will pause until it is plugged in. Again, its possible that the initial sync has different requirements, so it may want power for that as well.
I would suggest connecting the phone to wifi tonight and leaving it plugged in.