No it isn't true. Jehovah can be found in several translations older and other than the NWT. In fact, JWs used to be fond of showing the name in the King James Version, the American Standard Version and others to people.
Perhaps the brag of the overseer is more akin to boasting that the JWs have been more prominent in the use of the name than any other group. (Kind of like if the USC Trojans were to say they put the "champion" back in Football - its a stretch, you get my drift)
In this sense the JWs may well be able to brag and they certainly are the largest and most prominent group in the world that use the name Jehovah.
Unfortunately for them, the name "Jehovah" as we all know is a mistake, a fabrication, is not reflective of the true pronunciation of the Divine Name nor was it used by biblical Jews or early Christians or even widely used by anyone before the 14th century A.D.
JWs make a fool of themselves to brag about the use of the name Jehovah.
-Eduardo Leaton Jr., Esq.
PS: Just wanted to add, JWs are very clever to obscure the use of the name "Jehovah" with the "use of a personal name of God" and thus leave the uncareful reader with the impression that the name Jehovah was used.
They will in an article that talks about the name Jehovah, say that this is based on the Hebrew Tetragrammaton and then point to uses of the TETRAGRAMMATON, inscriptons, carvings, or in the bible translations, etc.. They will claim that early Christians used the "divine name" or that the Jews did or that the disuse of the divine name arose through superstition. Pehaps these are true, but the divine name being used in all of these instances WAS NOT the name "Jehovah" itself but instead was in fact a variation of the hebrew consonants, YHWH, perhaps sounding like "Yabe" or "Yahweh".