Yes.
Is that what you believe our Founders intended?
Yes, as the common law definition of "natural born citizen" included children of aliens living in amity and under the jurisdiction of the local sovereign.
What do you think the purpose of the "natural born citizen" clause was?
To ensure that a naturalized citizen would not become president.
If you think about why the Founders would care, it might occur to you that they would care if a person had a non-citizen parent. Being a candidate for President is not an entitlement and is not a right of all citizens.
Qualification is subject to serious concerns about the loyalties of the candidate. Are you not concerned about the loyalties of a person who has a non-citizen parent?
Obama's father was a non-citizen. When Obama was removed from the U.S., was he still subject to the jurisdiction of the U.S. or could that jurisdiction have been questioned by other nations, such as Kenya or Great Britain? The Fourteenth Amendment recognized that simply being born in the U.S. was not sufficient to ensure citizenship.
The "natural born citizen" clause recognized that simply being a citizen is not sufficient to qualify one for the Presidency.