I was a US Army Infantry soldier in a front-line unit for over 4 years. First as a driver, then M249 Gunner, then Team Leader, and finally Squad leader.
Generally, no. Empty magazines were not something we were 'required' to track. However this varied from unit to unit as some types of weapon systems had more damaging or expensive 'magazines'. For example with AT-4s we would need to turn in the expended tube to receive more. Otherwise an officer would need to vouch(usually through some paperwork) that we shot the thing and left behind the launcher.
Since you are asking in the conventional sense of M4 or other rifle/sidearm magazines, I'll tell you that we generally trained and operated so that we constantly tried to conserve our ammo and equipment. In real war discipline is a critical determining factor of outcomes. As a squad leader I can tell you I didn't have a punishment for being 'short' magazines after my soldiers shot. However, training on how to do proper reloads where you pocket your mag is considered a fundamental. In a unit where combat is routine, especially in a place like Afghanistan where resupply costs lives, you can imagine how many magazines a 100+ company of Infantry could go through if they weren't disciplined. Also, certain weapons have magazines that are hard to come by in the Army Supply systems (m14, SASR, etc. Though I'm not sure if the army even uses the M110 any more). Lastly, serious shooters that rely on their equipment know the reliability of their mags. This causes them to know them as "theirs". Even going so far to give them a 'spa day' by unloading, cleaning, and letting their springs extend after a week or more of patroling.
If a guy is sloppy with his equipment he is corrected.
