Possible...
Hi guys, I am a vegetarian too, except that I do eat fish, sea-food, and eggs. In this country, most of the people will think you are crazy, however you can go to regular restaurants, and only order the rice and beans, with some fried plantains and the salad... For the dessert, have fresh fruits... You'll find very good juices as well. I f you stop at cheap cafeteria, ask for some Yucca con queso frito, which is manioc with fried cheese, quite good...
Basically there won't be any place where it is organised for veggies, but be creative and select from the menu, or become friend with the cook...