Nah, I don't think even the Duggers thought they were building an army. I have heard that there are some Muslim and Christian groups that want to win the culture wars by outnumbering their neighbors with the idea that "The more children I have, the more ability I have to impact the world for God." But the quiverfull movement isn't associated with a particular Christian denomination. To be fair, the Bible does use battle metaphors, but I'm pretty sure there are anti-war people among the quiverfulls. The movement does refuse to use birthcontrol, but as long as it is their choice and they take care of their kids, it isn't really that big of an issue.
"Quiverfull is a theological position which is held by some conservative Christian couples who belong to various Christian denominations, which see children as blessings from God. It thus encourages procreation, abstaining from all forms of birth control and sterilization."