Question about syncing? Help?

Ok so I set up iTunes on my HP 2000 with Windows 8. I had a few songs, apps and ringtones from my mom's computer that I synced, and I iTunes said it would delete them upon syncing with my new library, and I didn't really care so I agreed. I know I can only sync with one library, but I recently downloaded apps from other Apple ID's on my phone (not synced, I manually signed into the accounts and downloaded them), and I've been wondering, if I decide to sync with my computer again, will the downloaded items be deleted?