The correct answer to this question is very complex.
Why?
There were laws which allowed or didn't allow Nicholas II to abdicate in 1917. And, there is debate as to if Nicholas II could abdicate.
There were laws which allowed sucession, those who followed with the right to rule Russia after Nicholas II.
To add to this mix, it is believed that Nicholas II abdicated twice.
The first abdication, which was destroyed, was said to have stated that Nicholas II had abdicated in favor of his son Alexei.
Let me note here that earlier documents had been signed and agreed upon that Nicholas II's sucessor was Alexei and his Regent was to be Nicholas II's brother, GD Michael.
If this first abdication is accepted as the one and only abdication then Alexei did become Tsar of Russia in 1917 and since he was under age, GD Michael became Regent.
If the first abdication is accepted then Nicholas II lost all rights and power as Tsar and everything in Russia fell under Regent Michael. And, Nicholas II held no power and henceforth would need to gain farther permission of official business from Regent Michael.
Nicholas II changed his mind and the first abdication was destroyed. This was not legal and so is debated. However, the abdication no longer existed and was physically gone.
Nicholas II drafted and then signed what is known as the second abdication. In this he by passed Alexei and gave the crown to his brother GD Michael.
The reason Nicholas II gave for by passing Alexei was not one that was acceptable and would prove as another debating point for those who believed Alexei was Tsar.
If the second abdication is legal, and the first abdication was not, then Alexei never was Tsar of Russia.
GD Michael became Tsar of Russia if the second abdication is legal. And, it appears that this was the accepted abdication by all those concern, including the Duma and GD Michael who took up the reins of Tsar.
Therefore, if the second abdication was accepted then Alexei was never Tsar.
If the first abdication was the one that was legal and binding, and the second abdication was not legal, then Alexei was Tsar from March 1917 with GD Michael serving as his Regent, until he came of age, which I think was 16. So if the first abdication was the legal document, when Alexei died, he was the uncrown Tsar of Russia.
Confused?
I am not very knowledgeable on this subject but I'll try to answer any questions that I can.
Hopefully, other posters will help explain what I can't.
AGRBear