as an interim measure, until someone who knows, comes along, i'll offer my thoughts- working from my very basic level of info on the army and navy (picked up from friends and relatives).
i'd think that you'd have a couple of areas to consider, food wise- for a start- before you start on the ethics of leather boots and the whole 'dynamic harmlessness vs being expected to kill other people when deemed neccessary' stuff.
depending what you're doing and where you are, your meal options are gonna be very different. i know that vegetarianism is catered for in the forces- under religious meals, in the UK and the States, but i doubt it stretches as far as veganism easily. i don't know if they'd take you on as a vegan, but they'd take you as a veggie, and i guess you could try and be minimal about eggs and dairy.
i think if you're living on base, working in your home country or a station abroad like germany, you might be fed en-mass, in a canteen, in which case i'd think there would most likely be some degree of choice, so you might have a few options- all be them perhaps simple ones (veggie curry and chilli, rice, pasta, veggies, fruit, bread, etc).
if you're in a situation where you're doing regular hours on base, and kinda 'commuting' (as a 9 to 5-er, lol.. i'm sure some people do this, like office staff, etc?!), and eating at home, you'll get whatever you or your partner/housemate cooks, so no problem there if they're vegan friendly. some stores on base and in military housing estates even carry amys meals, (even the ones in germany!) from what i've read!
but if you're on active duty, on manuveres (sp), on a 12 day march across some bog, or in a war situation, things'd no doubt be different. if you were using 'ready to eat' meals (the ones in sachets that you put in your backpack and add water to heat them) and if you could afford to be picky and had a degree of choice on what meal packs you got (dependant on what everyone else picked, how close you were to the front of the queue, what you could swap, or what was available) you'd probably get one or two meals that passed as close 'enough to vegan' outta the choices they generally have. this page (all be it from 2003- don't know whats changed since then) seems to agree with this:
http://www.vegparadise.com/news31.html
i know that in the Uk the 24 hour meal packs that 'accidently' turn up on Ebay, offer a few pretty palatable vegetarian options, but i bet eating the same few things over and over wouldn't be fun- and if something happened and your troop ended up with crates of meal rations that were solely baked bean and sausage breakfasts, beef chilli lunches, and chicken stew dinners, you'd have to eat it, or be hungry, and risk dying, or at least getting in big trouble with your commanding officer, i'd think.
if you're somewhere like the middle east, and set up for a long organised stay, you'd probably not be using meal packs, you'd have a cook and catering team in your camp (depending on how many were in your team). he/she/they would probably cook based on staples supplied by the army/navy/airforce back home, and suplimented by whatever was available locally. if there was plenty of fresh fruit and veg around, that'd be great- maybe do-able... but you still gotta think that in some circumstances you'd need to account for about 3,000 calories a day on that. if there was bread, and not much else, i don't think you'd do well trying to ask about mono and dy-glycerides, or last too long being too picky.
i remember looking into this a while ago, out of curiousity, and coming across a forum where guys talked about ww2 experiences. i'm pretty sure i saw a post from some guy who's dad was vegetarian in the forces then, and he said it wasn't fun at all and that he mostely lived on vile packaged cheese, and crackers. hopefully things have changed a lot since then, but i can see it still not being an easy thing to do, in a lot of situations.
eta: you could also supplement your rte meals with ones you've bought yourself from hiking/camping/space food companies (i've heard that many non veggies in the forces choose to do this), which might help a bit. but there is always the situation where you're in the arse end of nowhere, and you've run out of rations, and you don't know when you'll be back home- soldiers are trained to catch and prepare their own food in survival situations- and carrots and twigs and berries might not cut it then.