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 Sahih Muslim 711 b

Sahih Muslim 711b
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Translation
Ibn Buhaina reported

The dawn prayer had commenced when the Messen- ger of Allah (ﷺ) saw a person observing prayer, whereas the Mu'adhdhin had pronounced the Iqama. Upon this he (the Holy Prophet) remarked: Do you say four (rak'ahs) of Fard in the dawn prayer?