Yes, it is permissible to do so. One of the descriptions of the imam of the congregational prayer is adalah, which means observance of the religious rulings and not breaking them. If a person committed a sin by which he is no longer considered adil, but he repented after that and decided to refrain from committing the sin again, then he can be considered adil again. Also, the imam's recitation of the two chapters of the Quran in the first two raka'ahs should be correct and according to Arabic grammar.
The individual - that did not reach the level of Ijtihad - can not guarantee the correctness of his deeds before Almighty Allah, unless they correspond to the verdicts of a religious jurist - Marja since s/he will then, not be responsible for the errors in the verdicts - if any. Without following, the person will be held responsible before The Almighty if the actions and transactions were not really in accordance to the religion.