Well, AFAIK ROM 3.1 is patched during boot and it's seen by the system as Kickstart 3.9.
But what system are you using? Kickstart 3.9 or AmigaOS 3.9? I think the question was about the operational system. So the issue raised by Heiroglyph about 3.0 Kickstart and 3.1 Workbench option is clear that you can't mix them. OS 3.1 is OS 3.1 and it does not matter if it is on patched or non-patched ROM 3.0 or 3.1.
Just my 2 cents.