No it could not, since the people you mentioned enjoy diplomatic immunity and are not subject to the jurisdiction of the United States. Per U.S. law and the 14th Amendment they are not citizens at all.
OK...disregard the diplomatic credentials. Suppose two Chinese exchange students on student visa have a child in the U.S.. They return home when the child is one. At 21, the child returns to the U.S. on a Chinese passport and asserts his U.S. Citizenship based on the 14th Amendment, and obtains a U.S. Passport. 14 years later, is that person eligible to run for president?
I'm guessing you'd argue that he/she is...and I think you'd have a reasonable case; however, I think there are also arguments that could be made against it...