Has anybody ever lost weight just by eating fruits and veggies?

I looked up this diet called THE PALEO DIET, which is basically meats,veggies, nuts and fish, but i really dont understand it, so if I come up off of fried foods, potato's, beans, starch, bread,rice, noodles,pasta and cereal and work out regularly i will lose weight? i used a BMI calculator and it said i am obese for my height and weight. i am 194 pounds and I'm 5"6. my BMI is 37.3 ...and what about cutting back on sugars as well, using splenda or truvia? do you reccomend i make my own dink out of blended fruits,with no added sugars?