I'm going to guess no. Did you notice? When we're not Crossing, we can't physically be hurt. It just doesn't happen. But discomfort, seems like that's still a possibility.

[Need sheds her knee-length wool tunic too, appearing oblivious to Frieda's gaze. She's got a kind of quilted vest on underneath it, over an undyed long-sleeved shirt. The padding of the vest suggests a figure that's ever so slightly better-endowed than she actually is.]