Should I join the Marines?, or am I thinking irrationally?

Well, only you know the real motivations behind why you want to join and whether or not you will really benefit from it, but if this is what you feel you need to do right now, then you shouldn't let things stop you and you should go for it. However, if you are doing it to escape, or because you have given up on life, then maybe you should take some time to really think about it and whether it is the right path to follow. Talk to friends and family, and take their opinions into account too. You do seem to have a good idea of what will happen during the training, but it isn't a magical fix for your problems. You will still be you, you will just be you and also be a marine. Whichever way you decide, good luck.