Yes, its possible.  And,If you have a letter saying OK from USCIS, then thats the golden ticket, keep it with you.

My friend is a GC  holder n she has a child from a no paper guy. They don't live together but the guy pays child supports every month.

Once the guy selected for DV, he requested my friend to play a drama. That was his lawyers suggestion.

He stopped paying child support. The girl took him to the court. The judge said to him to pay child support, he explained he is illegal. He is not allowed to work. The judge can't force him to work and judge can't speak about his status because it is a civil court.

The guy requested to waive all the nonsense bar to USCIS, and  also showed the civil court judge's decision, added all the hardship. The guy went to Nepal and he is here today.

He is a good man. Now, he pays child support legally. Good for him, good for the woman, and best for the child.

So if you have drama in your life, use it.

Good luck!