Maybe. One thing to like about the "melting pot" analogy is that people from one culture exposed to a different dominant culture don't just retain their distinct character as if it was like the pieces of carrot in a salad, they are altered by this experience.

Chicken Tikka Masala didn't exist in India. And if you went to any British restaurant in 1900 they wouldn't serve this dish either. But in a British Indian restaurant today it's a staple because at some point (when and by who is debated) somebody in one of those restaurants was like "We should make a sauce to match local tastes" and it was created.