I know we will never know, but I find it hard to accept that Nicholas would have allowed the detested Vladimiriovichi to become his heirs. Surely he'd have done something. Wasn't there something in the works, or rumored to be at one time, where Dmitri would marry Olga and they'd rule as a team? That may have been a good thing for Russia if it had happened.
I also agree with Ra Ra Rasputin, that with the womens' rights and suffrage movement about to explode in the late nineteen teens to twenties, there would have been no way the old law would have been accepted or held up to the test of time. As someone mentioned, Alexander III made the call to demote certain members of the family from Grand Dukes to 'princes' so this would have been even less of a change.
Now, some royal houses have even given the throne to the first born, period, male or female. I believe in Sweden, they have a daughter who is older than the son, and she is in line for the throne. I don't think Russia would have done that, but allowing for a daughter if there is no son would have worked. She was, after all, his direct genetic heir, much closer than a second cousin!