“Haredi” means whatever the Haredi wants it to mean. They can opt for the peyot, beard and all, or not, depending on the individual. I don’t think they’ll issue them a khaki kaftan, though. But I have seen Haredi female soldiers dressed in a khaki below-knee-length dress with long sleeves.
Since some religious authorities permit being clean-shaven, there should be no problem.
More insight:
http://www.viciousbabushka.com/2012/07/insiders-guide-to-the-idf-nahal-haredi-battalion.html