Yes and No. First no, if for some reason, the entire Earth was destroyed... wouldn't the "underground metal tomb type thing" be destroyed too? But apart from that Scientology does not teach Armageddon or any other "end of days" type of belief. Life goes on forever.
But what this most likely is referring to is a huge storage in New Mexico where all of L. Ron Hubbard's works are preserved on high-quality material. ABC News show 20/20 was reporting about this in 1998 and was allowed to film there. The reporter said in the end: "Seen here for the first time, thousands of metal records, stored in heat-resistant titanium boxes and playable on a solar-powered turntable, all containing the beliefs of Scientology's founder, L. Ron Hubbard." The Washington Post, which also wrote about the not-so-hidden place in 2005, added:
"Other religions preserve their sacred texts. Nothing strange there." and as a funny note: "Scientology leaders apparently just don't want to misplace theirs".