Must the time for prayer begin for ablution to be valid and for one to lead the prayer if one is required to perform ablution for every prayer?

The ablution (wudu') for those with excuses (adhaab) is performed after the prayer time begins, because it is a purification necessitated by circumstance and is time-bound, similar to tayammum. Leading the prayer (imamah) by someone who has an excuse similar to yours is valid, though disliked by a group of scholars, because their own prayers are valid for themselves without needing to be repeated. And if excuses are pardoned for the individual concerned, they are also pardoned for others.