The Minchas Chinuch raises the issue, debated among many later Achronim, of whether a katan who becomes bar mitzvah in the middle of sefirah can continue to count with a bracha or not. There are a number of factors that this issue might hinge on:
1) Is each day of sefirah an independent mitzvah to count that day, or is there one mitzvah to count 49 days?
2) Does the act of a katan count as a kiyum mitzvah, or does it not count (no pun intended) for anything?
The nafka mina between these approaches would be a case of someone who converts in the middle of sefirah. If each day is its own mitzvah, then once the covert becomes a Jew he can count with a bracha. If the issue hinges on whether the act of a katan counts as a kiyum mitzvah, obviously in the case of an aku"m, he has no kiyum. These are not mutually exclusive approaches to the question or even the only approaches one can take.
I wanted to call attention to the novel chiddush of R' Ben Tzion Aba Shaul (in Shu"T Or l'Tzion vol 1) in addressing this issue. We usually think of the mitzvah of chinuch as something that applies only to a child. Not so, he argues. He points to the following source m'doraysa for the mitzvah of chinuch (and I believe R' Shachter holds this way as well) from the parsha of shema (Devarim 11:5)
וְשַׂמְתֶּם֙ אֶת־דְּבָרַ֣י אֵ֔לֶּה עַל־לְבַבְכֶ֖ם וְעַֽל־נַפְשְׁכֶ֑ם וּקְשַׁרְתֶּ֨ם אֹתָ֤ם לְאוֹת֙ עַל־יֶדְכֶ֔ם וְהָי֥וּ לְטוֹטָפֹ֖ת בֵּ֥ין עֵינֵיכֶֽם
Rashi comments:
ושמתם את דברי וגומ׳ – אף לאחר שתגלו הוו מצויינין במצוות, הניחו תפילין, עשו מזוזות, כדי שלא יהו עליכם חדשים כשתחזרו. וכן הוא אומר: הציבי לך צייונים
As Ramban there and in our parsha of Acharei Mos writes, even mitzvos which are chovas ha'guf are ideally meant to be fulfilled in Eretz Yisrael. The purpose for us continuing to fulfill them in chu"l is training -- chinuch -- so that when we return to Eretz Yisrael and resume living the way J are supposed to live, the practice of mitzvos will not be strange to us.
This pasuk, which is the basis of the entire concept of chinuch stems, is speaking to us as adults!
From here R' Ben Tzion Aba Shaul makes the next leap. Just like a katan, whose kiyum mitzvah is by definition incomplete, must nonetheless do mitzvos because of the chiyuv of chinuch, so that he is prepared to fulfill them properly when he will be able to achieve a full kiyum, so too, a gadol also has a chiyuv of chinuch to carry out a mitzva,h even if under the circumstance he is in he will not get a full kiyum.
The child who becomes bar mitzvah and is now a gadol may not get a kiyum mitzvah of sefirah if he continues and completes his count. Nonetheless, he must continue to count m'din chinuch.
He brings a proof from a famous safeik raised by R' Akiva Eiger (on OC siman 186). A katan ate a full, satiating meal just before he turned bar mitzvah. He said birkas ha'mazon. The sun then set, and he became a gadol. He is still full from that meal that he ate before sundown. Does he have to bentch again?
The "lomdus" behind the question is how to understand the chiyuv of bentching. וְאָכַלְתָּ֖ וְשָׂבָ֑עְתָּ וּבֵֽרַכְתָּ֙. Is the chiyuv of bentching because of the וְשָׂבָ֑עְתָּ, which is the state the now over-bar-mitzvah finds himself in, or is the chiyuv because of the ְוְאָכַלְתָּ֖, which was done while he was a katan and is therefore essentially meaningless? (There are slightly different permutations on this formulation as well, but this suffices for our discussion.)
The Ohr l'Tzion makes a fantastic diyuk that I haven't seen elsewhere. Why does R' Akiva Eiger frame the question as a case where the katan ate -- AND BENTCHED -- and now became a gadol, and now the issue is whether he has to repeat bentching? If what I just wrote in framing the safeik is correct, R' Akiva Eiger could have framed the same question in a simpler way: a katan ate to the point of וְשָׂבָ֑עְתָּ and now became a gadol -- does he have to bentch or not?
It must be, says the Or l'Tzion, that R' Akiva Eiger took for granted that in that simpler case, where the katan had not bentched, there is no safeik. In that simpler case for sure the now over-bar-mitzvah gadol has to bentch. M'mah nafshach. If the chiyuv for bentching is וְשָׂבָ֑עְתָּ, then he is chayav m'doraysa. But even if the chiyuv is for the וְאָכַלְתָּ֖, which was done when he was a katan, he is still chayav to bentch as a gadol, not because of a din in birkas ha'mazon, but because of the din of chinuch. Same with sefirah: even if there is no kiyum mitzvah as a gadol m'din sefirah, you have to count because of chinuch.
I love the diyuk, but I'm not sure I am convinced. To the point of why R' Akiva Eiger opted to set up this question davka using the more complex case, recall that I started the post with two approaches to the safeik of the M.C. One of the potential issues is whether the act of a katan counts as a kiyum mitzvah. R' Soloveitchik and others point out that the Rambam holds that if a katan registered (minuy) to eat a korban pesach, he does not have to bring pesach sheni if he becomes a gadol in between. He fulfilled his mitzvah with the act he did as a katan. The point is open to debate. Maybe R' Akiva Eiger wanted to roll this issue into his safeik. Had he given the simple case of a katan who ate וְשָׂבָ֑עְתּ and did not bentch, one might have gotten the impression that had the katan bentched, there is nothing to talk about. If he bentched, the kiyum mitzvah of a katan suffices. Not so fast, says R' Akiva Eiger. The safeik still stands even in that case. One can still debate the point.
In other words, the reason R' Akiva Eiger uses the more complex case is not because (as the Or l'Tzion argues) the safeik ONLY applies in this case, but because the safeik applies EVEN in this case. R' Akiva Eiger was not convinced that the act of a katan can count as a kiyum mitzvah.
Let me try prove to you that this was on R' Akiva Eiger's mind here. R' Akiva Eiger adds a note to look at the MG"A in 267:1. The MG"A quotes a Mordechai that says you are yotzei the mitzvah of kiddush recited during tosefes Shabbos even if tosefes Shabbos is derabbanan (comes up all the time if you make early Shabbos). Time inevitably passes; Shabbos will inevitably arrive; therefore it being a bit early is not a show stopper. Asks the MG"A: why then can a katan not be motzi a gadol in bentching? So what if he has no chiyuv d'oraysa -- it's just like tosefes Shabbos. Time will inevitably pass and he will ultimately have a chiyuv d'oraysa. However you resolvedthis question of the MG"A, the point I want to make is why R' Akiva Eiger alluded to it here. The issue MG"A is raising is whether a kiyum mitzvah derabbanan (tosefes Shabbos, katan who has no chuiyuv d'oraysa) counts towards a kiyum d'oraysa. I think R' Akiva Eiger chose his complex case deliberately to roll this issue into his safeik.
