No, it doesn't work and probably doesn't make sense.
Babies come into the world with a preference for sweet tastes.
Because most pediatricians suggest starting with rice cereal given in the morning and evening, I think the next logical step is fruit. Cereal and carrots for breakfast doesn't have much appeal for me. Be careful as you add bananas because they can be constipating. I usually suggest that you add them as one of the later fruits. When you do add vegetables, most advisors suggest adding yellow vegetables before green vegetables.