What people have to remember here is the fact that the Russian Monarchy was, even from the very begining, an overwhelmingly christian monarchy. And this was not just symbolic; it effected every aspect of a Tzars life,from the decision making process on down to family life, especially in the case of Tsar Nicholas II. And to say he was a man of the times, with the implication being that he must have done the sort of things a politician of today might have done in his youth,is really doing him a diservice. The other members of the royal family may have not lived according to the same high moral standards(they also were not expected to), but I think thats one of main reasons why both Tsar Nicholas, and his family, stood out from the rest of the nobility. It's also worth noting that Tsar Nicholas rarely let his children come in any contact with the rest of his family, outside of family gatherings and social events, because of their lack of disipline and morals.
What tends to be overlooked these days, and is crucial to really understanding who these people were, is that holding a position of leadership back in those times was never taken lightly by a Monarch no matter what country or religion the ruler was brought up in. And because of how close of a relationship the Orthodox Church had with the Russian Monarchy, this strict moral code was ingrained in them from early childhood. In the case of an heir to the throne, such as Nicholas, any deviation from this would have been sorted out and set aside early on in life. So its not a matter of "could there have been an illegitimate son?", its a matter of, would he have had a sexual relationship with someone he was not married to, given the fact that he was a devout Christian both before AND after his marraige to Alexandra(back then being a devout christian meant you actually abided by the law's of the church).
This may sound naive given the times we live in, but just because he was involved with another woman before marriage, does not mean he was involved sexually, and there is nothing about his character that has ever suggested otherwise.
There is a reason why there has never been a Bill Clinton-esque Tsar throughout the history of Russia, and it has to be understood that there never could have been.
