The Haredi public on mass does not enlist in the IDF - and not really because the "Torah Is their Living" (תורתם אומנותם) but because the IDF gets its orders only from the Israeli Government, and the "covenant with God" (not literal translation - BOT) is not part of their considerations. This is what I've been told by people who really understand Haredi thinking. That is why a Haredi politician can't act as a minister in the government...the Haredi public has for the last few generations gotten used not to do anything, big or small, without getting the decision of the "Gedolim".
In other words, the objection to the army is not about ruining the religious lifestyle of the young Bachurim. It is more about breaking the "Gedolim" monopoly of power in the Haredi world.