Yes, without a doubt, your body and its conditioning, is one of the most important means of survival in combat.
What army are you serving and what country? I have been deployed in Iraq and Afghanistan since 2004 and no matter where I was, there was some form of "equipment", now, it may have been sand bags,tires, or steel pipes, but there was always a way to work out. Also, I been on MRE's for over a month and they are purposely high in fat, a cheap way to keep your motor running,even the most remote FOB's have some type of mobile kitchen. Yes, the food sucks, but, its good enough to keep you from losing weight. Take command of you health, do what it takes to NOT lose weight, you will lose enough under the stress of combat. Sir, if you are a scout, trained as a scout, then you already should know this. Somewhere you training is lacking.
There are some excellent threads and advice on body weight exercises under the "conditioning forum", even discussions on training for military entrance exams. If you are looking for specific program for training, I would suggest the "bigger , stronger, leaner forum".
As for combat operations, its not so much you need to be in the best shape possible to to kill the the enemy, its to handle the stress of fear. They better physical shape you are in, the better you can handle fear and make the right decisions that don't get you killed. Good luck.