Will my iPhone re-download photos saved in iCloud after deletion?

Just to make sure we are talking about the same thing. You are not using iCloud Photos and only talking about your iCloud backup.

When using iCloud Photos, deleting them off your iPhone will also delete them from iCloud. If you are not using iCloud Photos, then those are stored in your iCloud Backup and after deleting your photos on the device, then the next backup will overwrite the previous one where those photos will no longer be available.

In either case you do have the option to restore the photos within 30 days from your Recently Deleted folder. The part that confuses me is when you refer to your phone "syncing". Not sure if you are referring to backing up to iCloud, or using iCloud Photos where they are synced across devices.

My recommendation would be to save those photos in another location first, then delete them from the device. You could use DropBox, a computer, or an external storage device:

• Transfer files from iPhone to a storage device, a server, or the cloud - Apple Support
• Archive or make copies of the information you store in iCloud - Apple Support

It won't work to save them in an iCloud Backup because once they are removed from your device, the next time your phone backs up, then will also be removed from the backup. You are more likely to inadvertently lose your photos.

PattiCee203 wrote: … save those older ones in regular iCloud backup - is it possible?

iCloud backup

         View and manage iCloud device backups - Apple Support

saves pictures Only If You Don't Use iCloud Photos. iCloud saves either in iCloud Photos or in iCloud Backup, not both.