Would a child born via in vitro fertilization be considered a dependent for Social Security benefits?

Sorry if the wording is odd, I couldn't figure out the best way to phrase it.

Let's say my mother and father both got eggs/sperm frozen in case something happens to them. My father contracts cancer and it's ruled that his health is a result of his service in the military. He passes away and several years later my mother decides to have his child via IVF. Would I then be eligible for things such as Chapter 35 GI Bill, or my mother be eligible for a Federal pension in my name?