A found this on the wikipedia of Prince Andrei Alexandrovich, GD Xenia oldest son:
Despite being only a Prince of Russia, he received a 21 gun salute at birth (which was usually reserved for Grand Dukes, with a 15 gun salute for Princes of Russia) at the insistence of his grandmother the Dowager Empress Maria Feodorovna
So, i think that the birth of princes also were celebrated.