As explained in my comments on the question itself: a restore is more than just the
.apk files. All parts of the system need to fit together, or you might run into trouble (unstable system, things not working as expected, apps crashing, and the like). There are different approaches to backup and restore, and one should not mix them without the required experience.
A Nandroid backup (as it's done by e.g. ClockworkMod) basically creates full images of all your device's partitions, without any abstraction. This does not necessarily mean one could not pick single items out of a Nandroid backup, but its not that trivial. If you restore a single partion only (such as
/data), it must fit the other parts of the system. The
/data partition also holds the
/data/dalvik-cache, for example, which consists of the byte-code for all installed apps, optimized for the ROM which created it. If you e.g. would restore the
/data partition from a backup of ROM-X to a device with ROM-Y, those DEX (Dalvik EXecutables) would not fit. Also ROM-Y might use different directory structures for several things, which are not reflected here.
You see, it would not be such a good idea.
Backups created with the
adb backup command are a different case: they are "abstracted". If you look into such an archive, you will not find the directory structure reflected. Thus at least in theory, an app backup (including the apps' data) created on ROM-X should restore fine on ROM-Y, as the ADB daemon on the device should take care of what belongs where.
Somehow comparable with the afore-mentioned ADB backup. TiBu uses its own format, and furthermore offers a "migration mode" when restoring backups from a different ROM. TiBu can also extract apps/data from Nandroid (and ADB?) backups, and hopefully fits them in fine even between different ROMs.
As you correctly noted: No, Titanium Backup is not needed to restore a Nandroid backup. The same script collection (Nandroid) used for the backup process would take care for the restore as well, again from the same place (ClockworkMod recovery). But as described above: Titanium Backup is able to read from backup files created with Nandroid.
As a last line, I want to repeat what I wrote in the beginning: Nandroid, ADB Backup, and Titanium are using completely different concepts. Though it is possible to mix them on a restore, this should only be done by experienced users understanding those concepts and knowing what they are doing.