Missing iPhone app (ipa) files after Library and associated files accidentally deleted

My entire "Music" folder (260 GB including four iTunes libraries and associated music, plus iPhone apps) was somehow deleted by my niece (MBPro, OSX). With the total deleted larger than the available free disk space, the "Trash" was empty. I used DiskDrill to retrieve as much of the deleted info as possible. However, all file names were lost. In the end, I was able to retrieve the main .itl and .xmp iTunes library files, some of the app files and most of the music files. Now, I am left with reconstructing the iTunes Library with which I sync my iPhone.

The reconstituted iTunes Library recognizes the iPhone (syncing off) and shows blank icons for all the installed apps. However, the links are broken for all apps. I've relinked all the apps I was able to retrieve, but most of the ipa files were corrupt.

My question is this…if I connect my iPhone and sync, will the apps that are lost in my iTunes (blank named icon still showing but with no associated ipa file) be copied from the iPhone to the Mobile Applications folder or will the apps be deleted from my iPhone because the actual app file is not in the Mobile Apps folder? At issue are a larger number of paid apps downloaded into my iTunes as gifts by my ex using my iTunes, but ex's iTunes account. I cannot re-download these apps since they were paid from my ex's account. Any suggestions?