No they don't, and if they did a King integraded headset would be no better than any other integrated headset, as its pretty much just a pair of bearings.
King IS trying to sell a retrofit HS for messed up frames with integrated headsets, but it requires special reaming with a special King reamer, and I have yet to see one in person.

Still, ride it until something happens. Probably around 7-8k miles on the roadbike on a single set of bearings. No appreciable wear to the headtube. If you're keeping that thing on the track, then it's a non issue.