What happens to the original photo file when I import it to Photos and have the "Delete After Importing" box checked?

Your question is not clear

Do you have a default managed library 9the Photos preference to copy imported items to the Photos library is checked) or a referenced library (that is unchecked) - a referenced library is strongly not recommended?

a totally separate question is what does delete after import do - it does what it says, after the import is complete it deleted the photos form the camera or iPhone - this also is not recommended since in some cases a crash can lose the photos in Photos after they are gone from the source - it is better to import the photos and verify they are safe and good and then after at lease one backu-p cycle has completed delete them form the device

and this article on file management in iPhoto may help you - it applies mostly to PHotos also - iPhoto and File Management

LN

It is suggested that you not use delete after import and that you not use a referenced library - unchecking the Copy imported items to the Photos library preference

I unchecked the "copy imported items to the Photos library" to save disk space.

That does not save one byte of disk space but it does create many, many problems - re-read the article on Photos and file management I linked to for details

LN

I unchecked the "copy imported items to the Photos library" to save disk space.

That will result in a referenced library. Photos will not copy the originals and manage them - it willI reference them simply in their current location (on the card, in the folder where they currently are). You are responsible to keep them save and manage them. I wrote a user tip on the risks of this set-up. See: Disadvantages of a Referenced Library in Photos

The delete after Import is only available when importing from a device -a camera, a card, an iPhone, but not, when importing files from a folder on the system drive.

You can delete local image files from your system drive yourself, after you imported them to Photos and they have been copied into the Photos Library.

I would never use the option "Delete after Import". The files will be deleted, before you can check, if the files have been imported correctly. Should you discover later, that some of the imported files are corupted and unreadable, it will be toolate o repeat the import, because the files have been deleted from the device. Or worse, if Photos should crash for some reason during the import, all photos will be lost, if you enabled "Delete after import".

Two possible solutions

1 - have your library on an EHD

2 - use iCloud Photo Library with optimized photos on all devices with limited storage

A referenced library is not a viable solution

LN