And Catherine the Great did technically have a claim to the throne via marriage.
Well, it was not just "technically". For the Russian mentality it was a very serious claim, totally legitimate. She followed the precedent established when Catherine I (born in the lower classes in the Swedish East Baltic territories) succeeded her husband Peter the Great in 1725.
And much more than that, she had a son, who was 100% legitimate direct hair to the throne of his father.
So in Russian eyes everything was absolutely OK.
Napoleon would be a minor officer in the Imperial army, so no dice.
I guess Napoleon might have been a genera in the Imperial army. The Empire valued brave and able warriors so he could have made a career like many a foreign officer did.
And he might have taken part in assassination of tsar Pavel. And he might have become a very influential general and politician. As a general he was definitely a genius, so he might go from victory to victory. He might become a second Suvorov. But that is his limit.
The Russian imperial dynasty was very strong, tsar Alexander had two brothers who were close to each other. Napoleon could not even become a king-maker, no way.
And really a Russian revolution in the 18th century is HIGHLY unlikely.
Sure.
The best case scenario for Russian Napoleon (if he is not killed in action) - he becomes too victorious and too proud of that, he is adored by the soldiers and he starts to think too much about himself. Tsar Alexander considers him as becoming to be too unmanageable and Napoleon is sent into honorable retirement with huge rewards and he lives the rest of his life in repugnant luxury.
The worst case scenario for Russian Napoleon - he starts to prepare assassination of tsar Alexander in favor of one of his brothers Nicholas or Constantine. But this plot is discovered at the very beginning (the tsar's brother might have reported him) and Napoleon is caught, tried and executed for high treason.