There is no issue with doing this, but if that person doesn’t join the congregation before rukū‘ of the first rak‘at then his/her right is voided.
Such fears and doubts are the insinuations of Satan. Don’t pay attention to that and attend the congregational prayer continuously.
It is better to recite tashahhud or other dhikrs while in tajāfi posture.
If other people consider you just then there is no problem for you to be Imam of congregation.