In the grand scheme of things, it was pointless for the Russians to overthrow their Tsar of the outcome was going to be practically the same under communism. All it did was cause hundreds of millions to starve and 45 years of tensions between the east and west.
Doubt it, honestly. Russia under the Romanovs was becoming insanely corrupt and filled with contradictions. As I was reading through some books, including one of my favorites about the Russian revolution, I became convinced that there was a graphene-hard wall of slavophilic ultratraditionalism standing in the way of any modernization efforts. It was highly reminiscent of France prior to 1789, where you had three classes all antagonizing each other: the nobility, the bourgeoisie, and the proletariat. France before '89 was pushed to the brink thanks to famine and mercantilism, whereas Russia had war and capitalism, which made everything so much starker and more explosive.
The nobility didn't want to let the capitalists gain any more influence; they viewed them with suspicion of being Westernized liberals. And the nobility were much less kind towards the working class than the capitalists, if you can believe that.
While coming under the control of Western liberals would have definitely spared Russia the famine, it probably would have doomed them come WWII (providing the lack of Bolshevism even allowed a fascist reaction).
And either way, the Romanovs would have been overthrown. In our timeline, it was radical proletarian revolution that killed him and his family. In an alternate timeline, it would have been radical bourgeois revolutionaries, much like the Jacobins who killed King Louis XVI, Marie Antoinette, and their son. So I think they were doomed regardless.
Nicholas himself was definitely going to be executed no matter who came to power. He just had too much blood on his hands. He all too willingly sent young men to the slaughter and allowed his officials to abuse them when they came back broken and disturbed by the realities of war. And that isn't even bringing up the repressions of Russia in the 1910s, which was an autocratic police state not unlike Saudi Arabia. I bet a lot of people don't even know that the GULAG and secret police originated in Tsarist Russia.
I still would have tried to save the kids ("kids", considering Alexei was 14 and Anastasia was 18), personally, because in the long term killing them just critically damaged the Bolsheviks' appeal, even if it allowed them to consolidate control in the short term. No matter the realities of modern corporate capitalism, it doesn't have the pre-requisite "we'll kill your kids" stain that communism gained. Hell, that's actually why Mao wanted to let Emperor Pu Yi lived, because the Chinese Communists were absolutely horrified by how brutal the Bolsheviks were. Most 20th century communist movements actually tried to distance themselves from the Bolsheviks precisely because of how they slaughtered the Romanov family. And like I said, you can say all you want "what about the kids killed by capitalism?" or "it was necessary due to the civil war", but that doesn't change that it fundamentally broke the appeal of the Bolsheviks even in the mind of revolutionary leftists. No matter how revolutionary you are, the cold fact is that most people aren't murderers and don't want to be one. That's why showing the Germans the atrocities of the Holocaust worked so well; even if many supported the Nazis, they didn't actually know what was being done.
If you showed most Westerners what poverty actually looked like in the undeveloped world, I'm sure many would have their faith in their system broken because when they hear "poverty", they think "lazy welfare-mooching ghetto queens who vote Democrat for more handouts" and not something like this. And it goes both ways. If the first thing a radical leftist sees as being the result of their new world is a bunch of butchered, stabbed, and sexually assaulted young women damned because of their social origin, they're going to stagger and say "I didn't sign up for this shit." And if they don't, their neighbor will, and there you have planted the roots of a new conflict.