Ummm, no. Everyone inside our boders is subject to our laws. The clause "subject to the laws thereof" is written to exclude the children of diplomats who have immunity and are not subject to our laws.
The original intent http://judiciary.house.gov/legacy/6042.htm
If that is true then why are illegal aliens not imprisoned for violating immigration law? They are simply deported back to their country of origin much like a diplomat who breaks a law.