And not the whole "yeah, Muslims are awfully queasy about their daughters marrying non-Muslims" thing?

Does having lots of female soldiers depress the need to find women in the local community, yes. Does the lack of American female soldiers make Muslim fathers in Iraq or Afghanistan willing to let their daughters date Christians? I suspect you'd find some who wouldn't mind as much, but it's a much harder sell compared to say, Germany in the post-war period.