I believe the earliest reference to ST being in the 23rd century was probably in The Making of Star Trek.
Yes, sort of. Here is the actual Roddenberry quote:
"In the beginning, I invented the term "star date" simply to keep from typing ourselves down to 2265 A.D., or should it be 2312 A.D.?"
Yet, several TOS dates clearly indicated 200 years from "now" (production time of TOS) which TMP somehow overwrote with Decker's "300 years ago" remark concerning the launch date of Voyager 6
in TMP (of course, Decker's memory could have been flawed).