Mavericks clean install with restoration from Time Machine Let's say I want to perform a Mavericks clean install like described in this tutorial. But what I also want to do is to keep all my older apps (especially ones not installed from the AppStore and all their data). I have OS X 10.9 developer preview. Is it possible to do a Time Machine backup, then perform clean install and then restore the data?

What would be the outcome of such operation and wouldn't it level the effects of the clean install (e.g. transferring some unnecessary system data) while restoring from the backup?
Your point about the restore from Time Machine leveling the effect of the clean install is correct. Unless you restrict yourself to just copying data files alone from a backup, while excluding custom application installs, application settings and system settings, a clean install would only mean spending more time with no apparent benefit.

As I mentioned in this answer to Is it better to upgrade to Mavericks or to perform a clean install?, a clean install is a tedious process that's better done only if you're having some issues in the system that you're unable to trace and resolve through other means.

Discounting bugs in OS X Mavericks itself, you would not notice any stability issues by going the upgrade path.

As a historical note, Apple used to provide an "Archive and upgrade" process long ago where the previous OS would be archived during the upgrade (this was during the time of Mac OS X Snow Leopard and before) and then moved to a straightforward upgrade process that has worked well for several years now.