Is the prayer of the congregants invalid if the Imam doubts the validity of his opening 'Allahu Akbar' (takbirat al-ihram) and repeats it silently without their knowledge?

The opening takbir (Allahu Akbar) is a pillar of prayer that is not waived by forgetfulness. Whoever repeats it invalidates their first prayer. However, some scholars are of the view that this is excused due to necessity, and they cite as evidence that it is permissible for the ma'mum (follower) to precede the imam (leader) in the takbirat al-ihram in some exceptional cases, such as when one performs the takbir individually and then joins the congregation, or if the imam doubts his intention and repeats the takbir discreetly. The Hanafis believe that the second takbir does not nullify the prayer, citing the hadith of Abu Bakr (may Allah be pleased with him) with the Prophet (peace be upon him) as evidence. Therefore, the prayer of the followers is valid, and one should disregard intrusive thoughts.