The short answer is no. The chow hall has a few vegetable options to choose from for each meal. These most often served vegetables include broccoli, peas and corn. Even if you’re in the field, and a chow hall is not available, recruits eat MREs (Meals Ready to Eat). Vegetarian MRE’s will always be available as an option. In fact, the vegetarian variety is often the MREs that no one fights to have, so you’re lucky in this case.
Please keep in mind that during basic training you will be burning a lot more calories than normal and you need to fill your body with carbohydrates and protein. Sometimes it’s difficult to extract the necessary amount of protein your body needs from vegetables (as compared to a meat eater). Therefore, if you’re a vegetarian, try to select vegetables that are high in protein like asparagus, broccoli, brussel sprouts, cauliflower and lentils.
Either way, don’t worry about your eating habits at basic training. Even if it is the tastiest food you have ever had, you will rarely get an opportunity to enjoy any meal.