Because the LiveSplit timer is not visible when playing in fullscreen (no, I don't have a 2nd monitor), I use Windowed Borderless Gaming so I can see the timer and make the game look like in fullscreen.

It is technically a third-party software, and they are not allowed, so will a run get rejected if I use it?

There is an alternative that doesn't use any third party software in the form of the "-popupwindow" launch option. If you're on Steam, you can set launch options by right clicking on your game in your library and going to Properties. Doesn't answer your question, but that's definitely allowed and I've run the game with that setting myself :)