From experience, I would NOT rely solely on Disk Utility. I can't count how many times I've had failing drives, but DU found nothing wrong until it simply didn't recognize the disk at all anymore.
This is correct -- DU does not test the drive data, only the file system. This is a tiny fraction of the total contents. It is *very* possible to pass the DU "First Aid" test yet fail a restore due to a bad block.
The following scenario can easily happen:
(1) You have a problem requiring full-system restore from a Time Machine backup
(2) Since this erases all drives being restored, you first run a DU First Aid on the Time Machine backup. It says no problems found.
(3) You commit to the restore, which erases all drives.
(4) After 5 min of restoring, the Time Machine backup encounters bad blocks and halts.
(5) You have erased whatever you had before, and now the Time Machine restore won't complete.
Since neither Time Machine nor Carbon Copy have a validation function, there is no way to inspect the backup quality except by restoring it to another machine.
The ScannerZ utility can force a read of the entire drive to verify all blocks are still OK: http://scsc-online.com/Scannerz.html
DiskTester can read all files on a volume to verify they are accessible: https://diglloydtools.com/disktester.html
However since drive space is relatively cheap, it might be quicker to simply clone the drive in question. That doesn't require specialize diagnostics, runs very fast and makes another copy of the data.