no, there would have been autopsy photos, kyle's face, dental records, finger prints, possibly DNA would have been all over police records and FBI records... from the first Kyle. With parents today doing things like prenatal genetic testing, saving core blood, etc, it's not a stretch at all that TS kyle would have left enough records behind for skynet to be able to put two and two together.
And it's not a plot hole, changing the timeline was the whole POINT of every terminator movie from the first one on. Terminator is not Trek, the continuity isn't sacred, continuity in Terminator is a plot device.