I have thought of this, and I think it would have been improbable that all of the family would have gotten out.
I think that the Emperor and Empress would have had to remain behind and would have suffered the same fate - death.
England was out of the question, as I believe the US would have been. The Fall of Eagles throughout Europe would have made any country unstable for heirs to a fallen throne.
I imagined that a remote area of Canada, a farm-style life, would have been best. I, like Robert Hall, considered the Vancouver area where the Russian emigre community was well-established would be a possibility. I think of someplace like Brasova, a self-contained estate, perhaps in Saskatchewan, Alberta, or British Columbia. While they would have still been nominally under the protection and as guests of the British Crown, they would be in a remote-enough area that "out of sight, out of mind" would have quelled the worst of the anti-Russian feeling of the British public.
I can envision Alexi proclaiming himself as Alexander IV, then immediately setting about to provide for the succession not by marrying, which would have been nearly impossible, but for the children of his sisters to inherit the throne in a similar fashion as the Fundamental Laws: first the sons of Olga, then those of Tatiana, then Maria, then Anastasia, provided they made equal marriages. Then the daughters of Olga, etc. (This is providing, of course, that all made it out. I'm of the opinion that only two or three of the Grand Duchesses would have actually made it out.)
We would still have a similarly murky inheritance picture as now: some of those sons and daughters would have married willy-nilly for money or love but not title. Others might marry into ex-ruling houses but insist that those "count." One or two would waddle their way to the front of the camera, wear absurd little crowns, and live off relatives. But at least the immediate opinion about inheritance would be answered to the generation of the grandchildren of the last Tsar.
I hope Maria would have married a soldier and renounced her rights. She did so want to marry a soldier.