Yes, there is a disease called Scurvy that one can get if they don't eat enough vitamin C, which comes from fruits and veggies. Scurvy starts with sore limbs, headaches and gets much much worse. A lot of sailors from previous centuries would fall victim to it as they only ate salted meat and hard tack (a sort of hardened flour wafer).

However, as long as you counterbalance your veggie intake with the lack of fruit intake, you should be fine.

It sounds like you could use more fiber in your diet to move things along anyways. Rumbling stomachs mean lots of digestive upset from lack of things moving smoothly along.