Bismillahir Rahmanir Rahim. Alhamdulillahi rabbil-'alamin. Was-Salatu was-Salam 'ala Sayyidina wa Azimina, Wa Habibi Qulubina wa Shafii Nufusina, Abul Qasim Muhammad. Wa 'ala Ahli Bayti tayyibina tahireen.
Is it recommended to perform Qada' of nafl/sunna prayers?
Yes. It is strongly recommended to perform Qada' of nafl/sunna prayers. Following Hadith narrations are proof for it
‘I went over to Abu Ja’far (asws) and I was a youth, so he (asws)
described the voluntary (Salāt) for me, and the Fasts. So he (asws)
saw the heaviness of that in my face, and he (asws) said to me:
‘This is not like the Obligatory (Salāt) which if one were to
neglect it, would be destroyed. But rather, it is the voluntary. If
you were too busy from it or neglect it, MAKE UP FOR IT. They (the
people) would be disliking if their deeds were to be Raised as
complete one day, and one day - deficient. Allah (azwj) Mighty and
Majestic is Saying (in Quran)
[70:23] Those who are constant at their Prayer,
and they were disliking if they were to pray Salāt until the day
declines, and that the gates of the sky are open when the day (starts
to) decline’.
Al Kafi V 3 – The Book Of Salāt CH 84 H 1 (page 18)
The following hadith narrations specify the total number of rak'ahs, both obligatory and optional, that must be prayed a day.
(It has been narrated) from Abu Abdullah (asws) having said: ‘The
Obligatory and the optional (Salāts) are fifty one (51) Rak’at –
from it are two Rak’at after the night (to be prayed) seated, counted
as one Rak’at prayed while he is standing. The Obligatory from these
are seventeen Rak’at, and the optional are thirty four Rak’at’.
Al Kafi V 3 – The Book Of Salāt CH 84 H 2 (page 18)
‘I asked Abu Abdullah (asws) about the most superior of what the
Sunnah has flowed with, from the Salāt. So he (asws) said: ‘The
complete fifty (Rak’at and one while sittingso 51 in total)’.
And it is reported by Al-Husayn Bin Saeed, from Muhammad Bin Sinan –
similar to it.
Al Kafi V 3 – The Book Of Salāt CH 84 H 4 (page 19)
In following narrations Imams of Ahlul-Bayt are strongly recommending to fulfill missed optional prayers
‘Abu Abdullah (asws) said: ‘Fulfil whatever is lost by you from the
Salāts of the daytime, at daytime, and whatever is lost by you from
the Salāts of the night, at night-time’. I said, ‘Can I fulfil two
Al-Witr (Salāt) during a night?’ So he (asws) said: ‘Yes, fulfil
Witr (Salāt), always’.
Al Kafi V 3 – The Book Of Salāt CH 85 H 3 (page 30)
‘Ismail Bin Jabir asked Abu Abdullah (asws), so he said, ‘May Allah
(azwj) Keep you (asws) well! Upon me are a lot of (outstanding)
optional (Salāts). So how should I deal with these?’ So he (asws)
said: ‘Fulfil them’. So he said to him (asws), ‘They are more
numerous than that’. He (asws) said: ‘Fulfil these’. I said, ‘I cannot
(even) count them’. He (asws) said: ‘Be at it’.
Al Kafi V 3 – The Book Of Salāt CH 85 H 4 (page 30)
Conclusion
Total number of daily rak'ahs is 50 (51 or 52). This includes obligatory and optional (nafl/sunna) rak'ahs. And performing Qada' of Optional (nafl/sunna) rak'ahs is strongly recommended (Mustahab).