Yes, yes you can. Even if you aren't reaching for your favorite candy or ice cream every day, you're still getting your "fix" through other foods containing loads of refined sugar. A study published in The American Journal of Clinical Nutrition stated that foods with high-sugar content (and high glycemic index placement) can be addictive. It all comes down to the way you have conditioned your brain to react to the introduction of sugar.
The process: When you eat sugar, your brain senses it as a reward, which makes your brain tell you that you want more. So, you overeat or take a second serving when you aren't even feeling hungry anymore. When refined sugars enter your body, your body breaks it down super fast. Even though fresh fruits also have glucose in them, they also contain fiber, which slows the process. So with refined sugars, you experience this big "high" right afterward, but then you crash. Your brain tells you to perk up by craving more sugar.
Read more: How to Cut Out Sugar Without Going Crazy
Sometimes it isn't so much the cravings, but the taste that gets you. Eating healthier foods will taste different. Your brain isn't the only working part that's been conditioned, but your taste buds, too. If you slowly replace your sugary snacks and treats with healthy choices, your taste buds will catch on. If you give it a chance, you'll be able to taste the sweet side of carrots.