Praise be to Allaah.
The rak’ah will count in Salaat al-Kusoof if you catch up with the first rukoo’. Based on what you say in your question, you caught up with the second rak’ah only, so after the imaam says the salaam, you have to do a whole rak’ah with its two recitations, two rak’ahs and two sujoods.
(See the description of Salaat al-Kusoof, Question#6111).
Sheikh Muhammed Salih Al-Munajjid