Can someone who wants to become a Catholic join the Church even though his invalid marriage causes an impediment to receiving Holy Communion?
The “impediment” you mention is the state of objectively grave sin. A person cannot enter the Church if he plans to continue living in such a state. Rather, he should cease living as a married person (e.g., live as brother and sister instead) until the marriage issue is resolved. That way he can enter the Church in the state of grace and fully live the sacramental life.
Contact your local pastor or RCIA director for more information.