The SMART data and manufacturer tools will tell you the health of the drive, but the drive has no idea if the data it's storing is corrupt or not. You need something at a higher level to determine if the bits on the drive are correct. The only filesystems I know that do that out of the box are ZFS and BTRFS, neither of which are supported by Windows.
For Windows, chkdsk will tell you if the filesystem itself has problems, but not the data within it. For that you need some 3rd party tool like an MD5/SHA1 checksum tool to generate the good hashes and then verify them for you later.