Sure, but that's irrelevant. The only questions are: are they sapient? And do they have free will? If yes to both, i.e. they can choose their own way, especially once Sauron's magical control is gone, then they are people.
Saying they aren't people because someone created/bred them for a specific purpose kinda feels like the people who argue certain dog breeds were bred for X or Y and therefore they should be culled/banned/etc. It simplifies the living creature too far and doesn't allow them to branch out from what they originally did. It's essentially genocide on the orc front.