Trump's mother was an immigrant who married and had children to become a citizen. He has 34 felony convictions. Under his own policy he's ripe for deportation to the UK.
Trump was born here - so no I don't think he meets the criteria. He wasn't an anchor baby and he was not naturalized.
I think you're forgetting his dad married an immigrant, who did not have her citizenship yet and probably married him for it. So yes, Trump actually is an anchor baby. But more importantly, so is Barron.