There isn't anything about boot camp that isn't training in some way or another.
I was in the Navy, not the Marines, but this is how we woke up:
0400
Drill Instructor turns on lights and starts hitting a garbage can with a club, yelling at us to get the **** up. If you are slow getting out of bed he helps you get out.
0401
You dress as quickly as possible and stand at the foot of your rack (bed) at attention.
0404
When everyone is dressed and standing at attention you are then ordered to strip your rack and then make it again, as quickly as possible. When you're finished you stand at the foot of your rack at attention until he's satisfied with everyones' uniform and their racks.
0407
If he's not happy with your rack then you do it again. Then you are ordered to go outside and form up in ranks.
0410
Once you're outside and formed up into ranks you march around a whole bunch to various places to do various things, one of those places might be the galley where you will get about 5 min to eat. In Navy boot camp you are not allowed to talk in the galley, you must use hand signals in order to ask for salt/pepper and hot sauce. Then you form up outside the galley in order to march around some more. If you (or anyone else) isn't marching correctly then you generally stop marching and start doing push-ups, or some other form of exercises.
Ahh, good times.