No. He was not a believer and he stood away from his father when they were boarding the ship. He was arrogant towards his father and disobedient.
And although Nuh pbuh asked him to get on the ship so he does not drown, he did not listen and arrogantly told his father that he will climb up to a high mountain and survive the flood.
( And ˹so˺ the Ark sailed with them through waves like mountains. Noah called out to his son, who stood apart, “O my dear son! Come aboard with us and do not be with the disbelievers. He replied, “I will take refuge on a mountain, which will protect me from the water.” Noah cried, “Today no one is protected from Allah’s decree except those to whom He shows mercy!” And the waves came between them, and his son was among the drowned.”) Hud 11:43
( Noah called out to his Lord, saying, “My Lord! Certainly, my son is ˹also˺ of my family, your promise is surely true, and You are the most just of all judges!” Allah replied, “O Noah! He is certainly not of your family—he was entirely of unrighteous conduct. So do not ask Me about what you have no knowledge of! I warn you so you do not fall into ignorance.”) Hud 11:45-46
لم يؤمن ابن نوح عليه السلام بدعوة أبيه ويحدثنا القرآن أنه كان منعزلا عن أبيه حين ركوب القوم في السفينة لكفره بالله وعقوقه لأبيه.
وَهِيَ تَجْرِي بِهِمْ فِي مَوْجٍ كَٱلْجِبَالِ وَنَادَىٰ نُوحٌ ٱبْنَهُ وَكَانَ فِي مَعْزِلٍ يٰبُنَيَّ ٱرْكَبَ مَّعَنَا وَلاَ تَكُن مَّعَ ٱلْكَافِرِينَ. قَالَ سَآوِي إِلَىٰ جَبَلٍ يَعْصِمُنِي مِنَ الْمَاءِ قَالَ لَا عَاصِمَ الْيَوْمَ مِنْ أَمْرِ اللَّهِ إِلَّا مَنْ رَحِمَ وَحَالَ بَيْنَهُمَا الْمَوْجُ فَكَانَ مِنَ الْمُغْرَقِين) هود 11: (43
(وَنَادَى نُوحٌ رَّبَّهُ فَقَالَ رَبِّ إِنَّ ٱبْنِي مِنْ أَهْلِي وَإِنَّ وَعْدَكَ ٱلْحَقُّ وَأَنتَ أَحْكَمُ ٱلْحَاكِمِين. قَالَ يٰنُوحُ إِنَّهُ لَيْسَ مِنْ أَهْلِكَ إِنَّهُ عَمَلٌ غَيْرُ صَالِحٍ فَلاَ تَسْئَلْنِ مَا لَيْسَ لَكَ بِهِ عِلْمٌ إِنِّيۤ أَعِظُكَ أَن تَكُونَ مِنَ ٱلْجَاهِلِينَ)
هود 11: 45 – 46