On Rosh Hodesh, the special insertion of "Ya'aleh V'Yavo" is added to the Amidah of all the daily Tefilot. The question arises whether to say "Ya'aleh V'Yavo" when praying Arbit early, before sunset, on Ereb Rosh Hodesh. While there is a precedent of Tosefet Shabbat, accepting Shabbat early, there is no concept of accepting Rosh Hodesh early. Nevertheless, the Sefer Eres Svi Frumer maintains that Ya'aleh V'Yavo is said. He reasons that since the Hachamim allowed praying the nighttime prayer, which is essentially connected to the next day, before sunset, that prayer has all of the qualities of the nighttime, including the aspect of Rosh Hodesh.
He proves his position from the fact that the Poskim never instructed not to pray early on Ereb Rosh Hodesh. If the Halacha would be that one cannot insert "Ya'aleh V'Yavo," they would have ruled that Arbit on Ereb Rosh Hodesh must be prayed after nightfall to enable the Rosh Hodesh addition. The Halacha generally does not warrant praying in a fashion that would prevent one from adding the special insertions. This is seen from the fact that that one should not recite the abridged version of the Amidah, called Havinenu, on Mosa'eh Shabbat, because it has no option for inserting the Habdalah addition of "Ata Honantanu"; rather, one must recite the full Amidah to enable the special addition. Therefore, in the case of Rosh Hodesh, it can be deduced that "Ya'aleh V'Yavo" may be inserted in the early Arbit.
This principle is also found in the Halachot of Purim, where the Mishna Berura (Rav Yisrael Meir Kagan, 1839-1933, Siman 693) rules that one inserts the special addition of "Al Hanissim" in Arbit, even if he prayed before sunset of Ereb Purim. Another precedent is the Halacha which enables inserting "Barech Alenu," the prayer for rain, when praying Arbit early on the day before the seventh of Cheshvan. From both of these cases, it is clear that early Arbit has all of the qualities and additional insertions, as if it were already dark.
If one prayed Arbit early on Ereb Rosh Hodesh, Ya'aleh V'Yavo is inserted, and there is no need to wait for nightfall.