There are several aggadic statements about the protective merit/value of Torah. (It should be noted, however, that it appears to have been a dispute amongst the Sages as to whether Torah provides protection; see Rabbi Dr. Yaakov Elman, "Righteousness as Its Own Reward: An Inquiry into the Theologies of the Stam," Proceedings of the American Academy for Jewish Research, Vol. 57, 1990 - 1991, pp. 35-67). At any rate, the charedi community wants to turn this into a halachic exemption from serving in the army and contributing to the economy. Furthermore, they expect all other Jews - even non-religious Jews - to accept this. They even present this argument to non-Jews:
Porush began by explaining the hareidi-religious view of Torah study. Israel survives in the hostile Middle East not due to the strength of its army, but due to the merit of Torah study, he told (French Ambassador to Israel) Bidot.
Well, as a religious Jew who will be sending his sons to the army, and who is (as a taxpaying citizen) sharing the financial burden of those in kollel, I think that we have a right to know the parameters of this protection. If you're claiming that it is a concrete benefit, which exempts you from concrete action while others serve instead and fund those in kollel, as concrete halachah, then I think that you should provide some concrete specifics.
1. Is this protection dependent upon time?
Does the protective effect of Torah even apply when the Torah student is not studying? Does it apply during the night? During vacation?
If yes - then why did many Gedolim urge their students to study during their vacation when various wars were taking place, or when there were even worse threats, such as the draft?
If not - then shouldn't the charedi community be learning in shifts, so that protection is kept steady around the clock, throughout the year?
2. Does this protection apply under all circumstances?
Bava Kama 60a-b indicates that a time of community-wide misfortune, Torah does not protect, and material steps are advised. Responsa Radvaz 2:752 greatly restricts the extent of the Gemara's ruling about Torah scholars being exempt from contributing towards security, including stating that it does not apply in cases where the rabbis consider themselves in need of protection. Rav Shlomo Yosef Zevin wrote that "If you understand that the scholars don't need protection in relatively peaceful times and are exempt from building the protective walls, what consequence has this when compared to a life-and-death struggle, a war which is a mitzvah and in which all are obligated?" So on what basis is the charedi community so certain that their Torah study protects from the clear and present dangers that exist today, such as to exempt them from serving the army?
3. What type of things does Torah protect from?
Based on the Gemara in Berachos 5a, the protection appears to be from physical illness. Other sources that speak about the protective value of Torah make no mention of specifically military threats, and indicate that it provides protection equally from illness, famine, etc. If that is the case, does that mean that the charedi community should receive less government assistance for medical services and other forms of aid? Otherwise, aren't they being hypocritical?
4. Is the protective effect more potent in the area where the Torah study takes place?
Presumably it is, because many stories about its alleged protective effect relate to the particular place where the Torah scholar/ tzaddik lived. But if so, why do the charedi yeshivos flee to safer places when war breaks out, leaving the residents of the city behind? If their Torah is providing any degree of protection, and they are doing their "military duty" in this way, then they should stay in, and even travel to, the cities that are under attack. Soldiers don't go where it is safe - they go where their services are needed, even at personal risk!
5. Is the intent of the person studying Torah relevant?
It's generally accepted that reciting Tehillim for the sick is only, or most, effective if the sick person's name is mentioned and/or "had in mind." Presumably, Torah study is likewise only, or more, effective if explicitly done with the goal of protecting those at risk. If so, then since soldiers are the ones most at risk, why don't charedim, when beginning their study sessions or dedicating their yeshivos, ever specify that their learning is to protect the soldiers? (The reason is presumably that charedim don't want to identify in any way, shape or form with the IDF. But if they won't dedicate their learning to protect the soldiers, why should they be able to claim exemption on the grounds that they are learning to protect the soldiers?)
The IDF can give precise answers as to the parameters of the effectiveness of their forces. If charedim are claiming that their Torah study is of equal or greater effectiveness, they have an obligation to do the same.
(Of course, the charedi community would never answer these questions, because they cannot do so without tripping themselves up. And the true answer to all this is that charedim do not really believe that their Torah protects. It's just an excuse, to cover their real reasons for not serving in the army: that it interferes with the way that they want to conduct their lives and society, and they feel no obligation to the wider Jewish community in this regard.)