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 712
Translation
'Abdullah b. Sarjis reported
A person entered the mosque, while the Messenger of Allah (ﷺ) was leading the dawn prayer. He observed two rak'ahs in a corner of the mosque, and then joined the Messenger of Allah (ﷺ) in prayer. When the Messenger of Allah (ﷺ) had pronounced salutations (he had concluded the prayer), he said: O, so and so, which one out of these two prayers did you count (as your Fard prayer), the one that you observed alone or the prayer that you observed with us?