Yes. Some recent research has determined that dogs are more omnivorous (able to eat and digest an assortment of foods) than carnivorous (able to eat and digest only meat and flesh). But keep the vegetables minimal, too much can cause icky poop.
I know a dog who not only will eat carrots but if not watched will pick and eat the ripe tomato out of the garden in the summer. he also loves corn on the cob green beans and fried tators . He also likes hamburgers, hot dogs, popcorn, ice cream (vanilla is his fave) and is healthy happy and smart. He gets regular dog food but loves grill out days.
Absolutely ! I once had a dog that loved carrots and any other crunchy produce such as lettuce leaves, celery stalks , raw potatoes , as well as apples and hard pears, she lived to be 18 before I had to put her down.