You are asking two different questions. No, tar, does not do its own crc. Most (perhaps all) modern tape drives will do a crc automaticly, or more likely, something far beyond a mere crc such as a two-level Solomon-Reed ecc. According to a brochure that I have here:
As for the table of contents, it is a fairly good way to verify a tar archive on tape. tar must read to the end of the archive to produce it.