All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If the Imam in reference did not recite the first Tashahhud and did not perform Sujood As-Sahw (prostration of forgetfulness), then, according to most scholars, he missed an act of the Sunnah, but according to many scholars, his prayer is not invalidated by neglecting Sujood As-Sahw. An-Nawawi said in Al-Majmoo‘: "As for the scholars’ opinions regarding the ruling on reciting the first Tashahhud and the sitting for it, our opinion is that they are acts of the Sunnah, and this is the opinion of most scholars as well." [End of quote]
Imam Ash-Shaafi‘i said in his book Al-Umm: "I do not see any evidence that it is obligatory on someone who missed Sujood As-Sahw to redo the prayer..." [End of quote]
Al-Mawsoo‘ah Al-Fiqhiyyah reads: "Missing out the acts of the Sunnah (in the prayer) does not invalidate the prayer, even if done deliberately, and it is not obligatory to repeat the prayer in this case. Rather, the ruling on it is that it is disliked without being sinful or punishable (Karaahat Tanzeeh), as stated by the Hanafi scholars." [End of quote]
Based on the above, according to the opinion of many scholars, the prayer of this Imam is valid, and so is the prayer of those he led in the congregational prayer.
As for the acceptance of this prayer by Allah, The Exalted, this is a matter of the Unseen which cannot be known.
Allah Knows best.