In episode 8, Pvt. Webster is looked a bit down on because he didn't bust out of the hospital while others did, leading the viewer to believe this was pretty common among the men of Easy Company. How common was this?
Also, when the hospital noticed a patient missing, would this lead to some kind of warrant? If their leaders found out they didn't escape to desert, but reported back to their unit to get back into action, would they generally leave it at that without taking further action?
There was another post regarding Dick Winters the other day, which I believe touched upon the very issue you're describing. If I recall correctly, it was basically made up for the show - the soldier in question received a warm welcome back.
I'd find the link but I'm on mobile right now. Don't think it's older than 7 days - definitely not a month. So you could try sorting by that and searching for Winters or Band of Brothers.
Hope this helps.