There is no evidence of any liaison between Nicholas and Hélène, although there is plentiful evidence of her involvement in a relationship with the Duke of Clarence who, ironically enough, had earlier proposed to Alix -- and been rejected. The entanglement of royal relationships gets extremely confusing, given the way the various names got linked in real or imagined matches.
In this case, it was the parents of Nicholas who favored the idea of a union between the French and Russian dynasties. But the princess herself does not appear to have thought much of it (perhaps because she was still getting over her disappointment in the quest to become the queen of England). That being said, the idea of becoming the empress of Russia had to have had some appeal to Hélène, since the British throne was out of the question.
In the end she, too, gave in to religious scruples, as she was a highly devout Roman Catholic who really did not want to abandon her church. As it was, she had to settle for the Duke of Aosta as a consolation prize. Indeed, it has been said that she expressed her frustrations over her failed quest to acquire thrones elsewhere, by spending her entire married life trying to get her clutches on the Italian throne. "Arrogant and affected, the Duchess liked to behave as though she were the real sovereign of Italy," was how one historian characterized her. Certainly the fact that she had a superior pedigree to Queen Elena could not but add to tensions in the royal court of Savoy.