Is the prayer of a follower valid if he prays behind someone who does not audibly say the takbir, and he only moves with him by feeling?

If the Imam is a latecomer, then following him is valid, but it is better to avoid it to avert disagreement. The prayer is not invalidated by the Imam not vocalizing the Takbir aloud; because it is a Sunnah and not an obligation.