There are only a very few states with a trailing spouse provision and I do not remember that NY is one of them. However, it never hurts to apply and see. The worst case scenario is that they say no, in which case you're no worse off than if you never applied in the first place. I could be wrong about what NY allows in this case.
It's not an appealable issue though -it's black and white. Either you are or you aren't. If you apply and they say yes, great. If you apply and they say no, then it's no.

