The Imperial family would've been devastated, no doubts there...
I think it would've proceed the way it was intended to be before Alexei's birth, c'est-à-dire Grand Duke Michael as Tsesarevitch, whether Alexandra like it or not, she wouldn't have had any choice this time. I wonder if the Tsar would've abdicated then instead of 1917...perhaps it would've been the best for him, his family, and Russia...
Maybe even today there would be a Romanov on a constitutional throne, like the Saxe-Cobourg-Gotha Windsor in England today, who knows?