I think the brown rice would work nicely. Just last weekend I used brown rice in a cold salad that I brought to a barbeque. I roasted a few chicken breasts, then diced the meat, and added it to the cooked rice with some shredded carrots and finely diced fennel. I dressed it with a citrus vinaigrette. I made the dish a day ahead and was very worried about how it might go over since most of the guests were not on a gluten-free diet. Everybody loved it. I think the flavor profiles that you mentioned (tomatoes, cucumbers, & basil) would taste even better than what I put together. Go for it, the brown rice will hold up perfectly even if made a day in advance.