The answer is decidedly YES. In New York state, a person is presumed to be the parent of any child born to or adopted by that person's spouse. But that only truly works if the parents' marriage is universally recognized in the US. But same-sex couples often find their rights called into question if they leave their home state.
These situations most commonly arise with lesbian couples, who, with the help of sperm donors, had their children without having to involve a lot of doctors or lawyers. If they are married, both women's names can go on the child's birth certificate in New York State. If the couple never plans to leave New York or one of the other states that recognize same-sex marriages, they are fine. But if they ever plan a trip to Disney World or the Grand Canyon, they may have their parental rights called into question because Florida and Arizona can be outright hostile to same-sex couples. Imagine what could happen if you are in a car accident and your spouse and non-biological child are injured and in the hospital. The lack of legal recognition of your relationship could keep you from being able to visit them and make decisions about their care. If you ever decided to move out of New York, you might find yourself unable to pick your own child up from school, or have your child covered by your employer's health insurance.
Marriage equality is spreading quickly -- as of this writing 16 states will recognize same-sex marriage once the Illinois and Hawaii laws take effect. But two-thirds of states still do not recognize our marriages, and in most of these states prohibitions on same-sex marriage have been written into the state constitution.
At this time, the best way to protect your family is to complete a second parent adoption. When the process is complete, the non-biological parent will have a court order confirming the legal parent-child relationship that all states must honor.