There is nothing in iReal Pro which will do this for you, however Keyboard Maestro and other similar apps can be used so you can script what you want to do. (Windows users often use AutoHotKey.)
For example:
Click this location (on the screen), select x from the menu (or arrow x times), wait for 0.3 seconds (while it does something), save, wait (while it saves), arrow to next song ... [then repeat until finished]
For simple scripts, you can set it to record and it records what you are doing, then you can stop it recording and test it with the next song so you might not need to know too much about scripting (at least in theory, depending on what you are wanting to do.)
You might be able to use Mac Shortcuts (Automator) to do this, although I have not looked into it.
I know Keyboard Maestro works because I found an old script I used with iReal Pro for something similar.
As Bob said, you should be able to find a PDF program to separate each page into individual files (make sure it automatically names each from the Song title. Otherwise if you get scripting (as above) to work, you can simply export a PDF in a script in the same way or within the same script.
Someone at George Mason might be able to help you with scripting.
[Just a comment here, for the script I created, the mouse location click relates to my size screen at a particular location, so I had the app full screen so if I ever needed to use the script again, it in theory would work with that click location (meaning a dropdown menu), although changing it is easy, which might be needed if the UI of the app changed since using it last.]