No one can give you an answer without knowing more. Your boyfriend's past is a factor but will most likely carry very little weight unless there are offenses against children or he is still using drugs. In most instances, these are idle threats designed to intimidate. You know, I wish I had a nickle for every blowhard ex-husband who stood around and threatened his ex-wife with the children, as if the children were a club with which to beat their mother. That attitude itself brings his ability to parent into question. How do your children get along with your boyfriend. Have they suffered any ill effects from being in contact with him. If not, tell your ex to go jump and don't worry about it. But if your boyfriend is still involved in the drug culture, has gotten you involved in it, and your children are demonstrably suffering because of it, you will lose them.
THE ANSWER PROVIDED is for general informational purposes only. This attorney does not intend to give legal advice. Evaluating the statutes and case law, as well as any relevant court documents together with a more detailed factual analysis could result in a different response. The attorney does not intend to create an attorney/client relationship by the response. Anyone seeking legal advice should always consult with retained legal counsel for a full evaluation of his or her claims.
There is no way to tell what a court will consider as significant, or to what degree they will consider certain facts as relevant.
In emotionally charges situations, such as this, as the previous attorney pointed out there is a tendency to throw idle threats at one another, and to angrily threaten to enforce things that perhaps may be unenforceable.
Overall, the Court will to some degree the full situation of all parties involved and how it would affect the safety of the child. Previous convictions and records may be taken into account, and generally are. If yo uare currently fighting for custody i would assume that you have an attorney or the court has appointed an attorney in yoru case, i would highly suggest that you speak to tha tattorney and gain further information as to the validity of these threats and potential for defense against them.