Ha, she that must be obeyed has spoken
To answer your question, no, the format is fixed.
I will ask one of my own though, why would you want a different format? We use OS/2 here on our workstations which means that the internal disks are formatted HPFS or JFS yet data from them is backed up to several NAS boxes without problems. We wlso have data on our NAS boxes from almost versions of windows, a couple of iPhones and several Android phones as well as a clients Macbook. Data is data (0 and 1), the file system takes that data and stores it that is all any hard disk does. It is an app that takes that data and displays it. Yes, the app might dictate a layout for storage but that is what you see in a file browser NOT how it is physically stored on a disk.
The problem you might have is getting your pictures from the iPhone to the NAS but since you have a Mac you should be able to do it as iPhone --> Mac --> NAS (we did it that way for our client). If there is an FTP app for the iPhone then you should be able to use that to transfer directly to the NAS as we do with the Android phones and tablets.