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If he was born before the Noldor went in Exile then he is indeed a High Elf but if he was born after the Noldor returned to Middle Earth then he is not a High Elf
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Somewhat of an unwritten postulate: children of High Elves are High Elves too, if only by inheritance of the title. They did not necessarily have to see the Light of Trees with their own eyes to be High Elves.
Even so, it seems likely that Glorfindel would have seen the light himself, being old enough to have came back, either with Fingolfin or Feanor, since by the Fall of Gondolin, he was established as a noble chief there.