In the context of the halacha not to fast throughout the month of Nisan, Massechet Sofrim[4] states that an exception is that bechorot fast on Erev Pesach. The Tur[5] and Shulchan Aruch[6] cite this practice as normative, and the Tur explains that it is in commemoration of the miracle that the Jewish firstborns were saved in Egypt.
The idea that one may eat at a seudat mitzva and thereby cancel the fast is debated among the Acharonim. The Magen Avraham[7] does not allow firstborns to eat even at a brit mila on Erev Pesach. The Mishna Berura[8] reports, however, that the minhag in his time was to allow eating at seudot mitzva, including the meal at a siyum. The idea that a siyum meal can serve this role as a seudat mitzva is found in the Rama[9] regarding the permissibility of eating meat and drinking wine at a seudat mitzva during the Nine Days.
In these contexts, there is room to distinguish between those people who are the main individuals involved in the seudat mitzva, for whom the day is like a Yom Tov, and the other participants. For example, one who is a sandek on the day of his parent’s yahrtzeit may eat on that day, even if he ordinarily follows the minhag of fasting on that day, whereas a simple participant in the brit may not.[10] Similarly, even those who do not allow firstborns to eat at another’s seudat mitzva are lenient regarding a firstborn who serves as the mohel or sandek, as well as the father of the circumcised baby.[11] In any event, the minhag is to allow all participants at a siyum to eat at the siyum’s meal, and as a result, to continue eating the rest of Erev Pesach.
The simple logic for this leniency is that each individual’s participation makes the celebration more special, thus heightening the ba’al simcha’s[12] event. Therefore, participation in the ba’al simcha’s meal is what is crucial regarding our discussion. Indeed, some allow even a firstborn who missed the siyum itself to take part in the seudat mitzva.[13] Following the logic that it is the enhancement of the ba’al simcha’s event that matters, the Minchat Yitzchak[14] says that even the Chavot Yair,[15] who rules that a meal held the day after the siyum was made is still considered a seudat mitzva, is discussing only a seuda in which the one who made the siyum participates.
The gemara[16] relates that Abaye was especially emotionally involved in the Torah successes of others, to the extent that he would make a party for the rabbis when a young scholar finished a massechet. Some[17] understand that the halachic status of such a party extends even to one who is not present at all at the celebration of the one who finished the Torah section; the vicarious joy of all those who are happy about the siyum is equivalent to their participation in the seudat mitzva. The Minchat Yitzchak[18] writes that according to this approach (which he discourages relying upon but considers legitimate), one can be considered a “participant” in the seudat mitzva even if he does not actually eat together with the main party.
In most cases, it would not seem logical to consider one who “takes part” in a seudat mitzva via Skype as being a halachic participant, certainly in regards to increasing the simcha of the one who made the siyum. However, according to the approach that anyone connected to the siyum is entitled to celebrate his happiness due to the occasion, it is at least somewhat plausible to say that witnessing the event via Skype is sufficiently significant.
A number of authorities take a surprisingly lenient approach about siyum standards for ta’anit bechorot,[19] relying heavily on the following two factors: 1) The fast is only a minhag. 2) For many people, fasting would have a significantly negative impact on the Seder. While not actually cancelling the minhag, some seem to lower the bar of who is included in the siyum, such that they enable almost anyone to eat. If one feels a need to be lenient, Skype participation can indeed be contemplated. If so, it is best to watch the siyum and celebrate it as a group, and/or to witness a siyum that brings one true simcha (e.g., based on one’s connection to the person or to the level of accomplishment).