A similar question would be, “if cheddar cheese didn’t have annatto (natural coloring) in it, would it still be cheese?
Annatto- “The small hard achiote seed, which is also called the annatto seed, is prized in Indian and Hispanic cuisine. It is native to Central America. Annatto or achiote seed is brick-red with a slightly bitter, earthy flavor and imparts a rich yellowish-orange color in Caribbean, Latin American and Filipino cuisines. Available whole or ground, the small triangular shaped seeds are used as both a spice and as a natural coloring in butter, rice, smoked fish and cheeses.” http://wholespice.com/annatto-seeds.html
It’s possible to buy cheddar with and without the orange food coloring called annatto. I prefer mine without, but it really doesn’t change the flavor one way or the other.
I feel like wise about other foods including ice cream.