This is actually a very interesting POD, though I doubt the boy would be named Constantine (more likely Alexander or Alexei). To begin with Nikolai II would have an heir near the beginning of his reign, one that would be of age, if barely, and able to assume the throne if things end up the same as OTL and around the same time. However a healthy boy in 1895 really changes things up.
First off, it was the lack of a son and heir over a 10 year period that led Empress Alexandra deeper and deeper into the realm of mystics and faith healers, most of which here charlatans and ending with Rasputin. With a healthy son right off the bat, Alexandra might not go headfirst into religious extremism, although considering her personality I'm not sure about it.
Second, Nikolai himself started out skeptical of his wife's religious extremes and only followed her lead when year after year passed with no heir and, eventually, when the awaited son was stricken with an incurable disease.
So even if Alexandra still goes off the deep end Nikolai himself might not, blocking the devastating influence of the false religious figures and eventually Rasputin.
Third, without shared grief over first the lack of a heir then over his illness, Alexandra's influence over Nikolai would be lessened. This also means that Alexandra won't be able to wield Alexei as a weapon to get her way, as she did OTL during World War I. A less influential Alexandra opens Nikolai up to alternative influences, such as the various Grand Dukes and his mother the Dowager Empress. This could lead to the family being able to convince Nikolai to grant at least some of the reforms Russia desperately needed.
In all, while such a change might not be enough to avoid the 1917 revolution, it does at the least change up some of the Russian landscape. Now whether or not this would be enough save Russia from Communist rule, I don't know.