Does the prayer of one who performs the opening Takbir (Takbirat al-Ihram) simultaneously with the Imam's Takbir for bowing become invalidated, if they are then unsure whether it was for the Ihram or for following (the Imam)?

If a worshiper doubts whether his takbir was intended as the takbirat al-ihram (opening takbir) or the takbir for bowing (ruku‘), then his prayer is invalid, and he must repeat it. This is because the takbirat al-ihram is a pillar (rukn) of the prayer, and doubting whether a pillar has been performed is equivalent to not performing it.