No Nicky, means Alexandra most likely doesn't go to Russia, ergo, no Alexei (or no OTL Alexei, rather. Since Alexandra is likely to have sons by her alt-husband who might suffer from haemophilia).
As to Marie never forgetting Denmark, I don't think that's entirely true. She certainly never forgot her family in Denmark, but she never tried to force the constitutional monarchy (as in Denmark and in England) idea onto Russia. Therefore, I don't think that George will marry a Russian aristocrat just because she understands Russia. And also, the aristocrats were (by that point) some so alienated from their estates due to the bubble life they had in St. Petersburg, I don't think it would do much good. Also, the problem with marrying into one aristocratic family is that you get every other aristocratic family ranging themselves against them due to the general rapaciousness.
AFAIK, Alexander II was planning to set the Pauline Laws aside (or some such) when trying to marry his morganatic wife equally. The Imperial Family was vehemently against it, and his morganatic wife was Dolgorukov (one of the oldest families in Tsarist Russia), so I'm not sure if George will be able to make any headway when the chief opponent is likely to be his mother (who was also ringleader of the opposition to Princess Dolgorukova).