The answer to your question is a resounding -- maybe...
Each and every day, you have a decision to make, a choice. Which desire is stronger in you? - the desire to lose fat and weight, and to improve your health? or the desire to consume a favourite food? There is no right or wrong, good or bad. Whatever you choose at the moment is just that, a choice, you make it, then live with it including any consequences.
The thing is, if you are confident you can keep control, then once you've been lowcarbing for a while -- fat and inches are being lost at a steady rate, then you might choose to fit an occasional serving of a favourite food into your program. A small banana has about 27 carbs. It's not like chowing down a bag of Oreos. On the other hand, if the sugary sweet fruits trigger cravings and sends your blood sugar and insulin into a wild yo-yo ride, then indeed you may have to choose to eliminate these foods altogether. My personal experience has been that after a few months, some old favourites just don't live up to the memory ... I've taken a taste, and thrown it out, wondering why on earth I ever liked it in the first place. I have new favourites now ..
On the subject of being hungry, the solution is ... EAT!! Lowcarbing isn't about starving and willpower and going without. Yes, you restrict carbs, but you can have unlimited proteins and fats. Have smaller more frequent meals and snacks. Boil up a dozen eggs, have small cans of tuna in the pantry, bake a chicken or make a roast. Keep it in the fridge, and when the munchies strike, grab some. Use seasoned mayonnaise and dijon as a dip.
You'll do fine, I know it ..
Doreen