Does the PhotoSync app permit that? I use it to copy files to my NAS but it has some USB-related options I never explored. I used to use Image Capture but heard of PhotoSync and have never looked back.
Example:
Original: IMG_9999.JPG
Server-side file: 2015.01.15__IMG_9999__.JPG
I’m not sure Apple allows any third party app to access the unmodified originals. Imagine you crop a photo to remove some embarrassing part. A third-party app can just recover that? What a privacy risk.
Of course this won’t matter if you don’t do any photo editing on iOS.