I doubt a single haredi man will put his life in danger. The idea of having to work is repulsive enough. BTW, more than 80% of haredi men in the US work for a living, as opposed to 30% in Israel. That's because the US government doesn't give them tax dollars with which to warm yeshiva benches.
First refugees travelling on Hungarian bus arrive at Austrian border (Reuters)
from the article: IDF freezes service deferrals for volunteering due to enlistment drop