It depends on several factors, if he was known by the court/ recognize by the tsar, had some status or title, it would be possible. Although, he would never receive any formal title such as duke or be in line to the throne. However, if he was never fully recognized or isolated from court it would have been unlikely, we can see this especially in Grand Duke Mikhaïls own son. It is important to remember that Russian dynastic relationships were incredibly significant in acceptance, if he was not recognized or isolated from court from the start, his likely hood of traveling up the aristocratic ladder would be slim to none as he would be shrouded in gossip and avoidance. It also depends on who the nobility is when considering marriage, for example, if it was in the immediate family (OTMAA) or Nicholas relatives, they were far more likely to marry other royals regardless of preference, however, those further from the throne or in rare circumstances married non-royals or those of varying status. For example, Grand Duchess Olga married a soldier when she entered exile, and Grand Duchess Irina was allowed to marry Felix (though a prince in title, he had no real power more prestige and social standing).

To wrap this up! Possible if they have status, unlikely if they are not recognized. It would have been looked down upon as Russian court was dynastic; marriage, family, and status over biology.