It is disliked to start a voluntary prayer after the Mu’adhdhin has started to say Iqamah for prayer, whether that is a regular sunnah, such as the sunnah of Subh or Zuhr, or anything else, and regardless of whether he knows that he will catch up with the rak`ah with the Imam or not
وَحَدَّثَنَا حَسَنٌ الْحُلْوَانِيُّ، حَدَّثَنَا يَزِيدُ بْنُ هَارُونَ، أَخْبَرَنَا حَمَّادُ بْنُ زَيْدٍ، عَنْ أَيُّوبَ، عَنْ عَمْرِو بْنِ دِينَارٍ، عَنْ عَطَاءِ بْنِ يَسَارٍ، عَنْ أَبِي هُرَيْرَةَ، عَنِ النَّبِيِّ صلى الله عليه وسلم . بِمِثْلِهِ . قَالَ حَمَّادٌ ثُمَّ لَقِيتُ عَمْرًا فَحَدَّثَنِي بِهِ وَلَمْ يَرْفَعْهُ .
This hadith has been narrated by Abu Huraira with another chain of transmitters. Hammad (one of the narrators) said: I then met 'Amr (the other narrator) and he narrated it to me, but it was not transmitted directly from the Messenger of Allah (ﷺ).