Absolutely. GO for it. Your legal status has nothing to do with it.
NYC EXPERIENCED IMMIGRATION ATTORNEYS
Phone: (866) 456-8654;
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
As the immigration attorneys have already said, this is a non-issue as far as the domestic relations court is concerned.
If you want to learn more about getting into court for child support, here is a self help link (below). If you need more information, or would like an attorney, there are plenty of attorneys listed on this site.
Besides obtaining child support, consult with an immigration attorney and see if you may get legal status by either a VAWA or a U-Visa. This should be done in person and not on a public forum like internet.
Khaja M. Din, Esq.
Din Law, LLC
Free Initial Consult For All Your Immigration Questions