If we go with the view that holds that "aliyah bechoma" can also be referring
to a mass aliyah and does not (necessarily) have to mean with respect to
(only) forming a government, one could argue the facts of what happened
here. That is, was there ever indeed a modern "mass aliyah" movement that
fits that definition precisely? I realize there were approximately 800,000
Sephardic Jews who fled the Arab countries in the late 1940's. 800,000 is
a relatively large number, but nevertheless does that necessarily fit the
definition of "mass?" Perhaps the concept of "mass aliyah" is referring to
at least more than half of the Jewish people making aliyah at one time.
Also, does the intent of the one's making aliyah matter vis a vis "aliyah
bechoma?" In other words, if it can be presumed that the Sephardic Jews
were fearful of losing their lives should they have decided to remain in
Arab lands, but not because they were intending to "force the end" by
assisting in creating a Jewish government, is that not a consideration
here? Also, from what I understand, those 800,000 were largely children,
perhaps not even bar mitzvah yet, sent by their parents via the "Youth
Aliyah" organization. Can one not say that as non-bar mitzvah age they were
not yet chayiv in mitzvot yet, and as such for such people to take action
which would be considered "aliyah bechoma" for adults, it may not carry the
same weight for Jews such as them, and we can say after-the-fact that their
residence in Israel is acceptable even according to those who hold their
action was "aliyah bechoma?"
Rashi says "together, with a strong hand". If we understand that each of these by itself is forbidden, then even if the Zionists were a small group, what they did is forbidden because they took the land by warfare.
Together or en masse has been defined variously by Zionist rabbis as the entire Jewish people (Rabbi Avraham Yellin), or the majority of the Jewish people (Rabbi Y. D. Blumberg).
The Satmar Rav in Vayoel Moshe siman 10 proves that it means even a large group. (However, it cannot mean a group of 42,300 or smaller, because that is the number of Jews who came up in the time of Ezra (Ezra 2:64) and the Gemora in Yuma 9b says that Ezra's aliyah was not called b'chomah.) Here is his proof:
The Midrash relates that whenever Reish Lakish saw large crowds of Jews in the market, he would say to them, "Scatter yourselves! When you came up to Eretz Yisroel you did not make yourselves a wall, and here you are coming to make yourselves a wall?" The Matnos Kehunah explains that Reish Lakish was speaking to large crowds of Babylonian Jews; the criticism that they did not make themselves a wall when coming up to Eretz Yisroel refers to the passage earlier in the Midrash - the same statement of Reish Lakish brought in Yoma 9b: "If you had made yourselves a wall..."
Now, from the fact that Reish Lakish saw a large crowd in a market in Babylonia and called it a "wall", and criticized them for not coming with similar crowds in the time of Ezra, we see that any large crowd, even if not the majority of the Jewish people and even with permission from the government, is called a "wall." For certainly this crowd seen by Reish Lakish was not a Jewish uprising, G-d forbid - that would have been forbidden under the oath not to rebel against the nations. Also, Ezra's immigration took place with permission from the king, and there was no rebellion, yet the Gemara implies that it would have been called a "wall" if only the numbers had been larger.
And it would be unreasonable to dismiss this story about Reish Lakish and the crowd by saying that the crowd in question was in fact the majority of the Jewish people. It is highly improbable that the majority of the Jews from the entire world would have gathered at one time in some marketplace in Babylonia. We know that after the destruction of the Second Temple, the Jews were scattered to the four corners of the earth. Rather, there was merely a large crowd in that marketplace, So this proves that any large group, because of its great strength, is termed a wall.
Rabbi Avraham Yellin attempts to prove from the Second Temple period that slow immigration over a extended period is not called "going up as a wall." Although the initial group that came with Ezra numbered only 42,000, certainly over the course of time more Jews came up, he assumes. So why does Reish Lakish say that the Babylonian Jews failed to come up as a wall? Clearly "as a wall" means all at once, not over an extended period of time. The Zionists, too, did not immigrate all at once.
However, it may well be that he is mistaken and there was never any second wave of immigration from Babylonia. Those 42,000 were the ancestors of all the Jews of Eretz Yisroel in the Second Temple period.This is in fact the contention of the Pnei Yehoshua, quoted in Vayoel Moshe Siman 12.
Even if there was more immigration, Yellin's proof is not conclusive, because it may be that there is a difference between "as a wall" when used in connection with the Three Oaths, and when used in connection with a time of redemption. When a time of redemption comes, such as the conclusion of the 70 years of exile foretold to Yirmiyahu the prophet, Hashem wants all Jews to respond and return to Eretz Yisroel right away. It is not enough that they eventually returned over the course of a century or two. But during exile, Hashem wants the bulk of the Jewish people to live outside of Eretz Yisroel. So even if they come to Eretz Yisroel piecemeal, like the Zionists, if the end result is that a large portion of the Jewish people is there, it is a violation of the oath
There were many ships bringing Jews to Eretz Yisroel during the last years of the British mandate that carried more than 1500 Jews each. And a few of these ships probably arrived on the same day or within a very short period. It is possible to imagine 42,000 Jews coming on one day.
However, if you learn that b'chomah means the majority of the Jewish people, which before the war would have been around 10 million, it's hard to imagine 10 million immigrants entering the land on any single day. That would be five or ten thousand huge overflowing ships. I therefore think it's obvious that if the majority of the Jewish people is required, it doesn't have to be on one day, in one week, one month, one year, or even one decade. If the majority comes, that's aliyah b'chomah no matter what.