Restoring iOS apps (+data) that weren't transfered to PC before iPhone backup
Full disclosure: I'm the lead developer of the repair software you're most likely referring to ;)

The data for the apps are stored in the backups, just not the apps themselves. Normally, the apps should be downloaded again automatically from the app store after you restore and setup (logging in to your app store account/AppleID). You don't have to have the apps themselves transferred into iTunes in order for their data to be in the backup.

So yes, normally if you repair it, the apps should reinstall, and the data for those apps should be there waiting after the restore. In the rare event (but does happen) that the app data that you need was part of what was broken in the backup, that's why we offer a guarantee with our software :)