No, not likely.
In a bankruptcy case decided on October 22, 2014, U.S. Bankruptcy Judge Marvin Isgur in Houston ruled that over $100,000 in attorney fees and costs incurred in a child custody dispute would not be discharged in the husband's chapter 13 bankruptcy case.
Even worse for the ex-husband, the court decided that the attorney fees and costs were a priority claim, and had to be paid in full during the bankruptcy plan because they were in the "nature of support" and therefore a "domestic support obligation" or DSO. The court allowed the priority proof of claim as a domestic support obligation. In re Beacham, Bankr. Court, SD Texas 2014.