Some background first
If by "focus range" you mean the minimum distance at which focus can be obtained, it isn't a feature of a camera body, it is a limitation of the lens on it. Using better terms, it is called minimum focus distance (MFD).
With a camera with interchangeable lenses (such as a DSLR), using a different lens will yield a different MFR. For example a few Canon lenses :
- 70-200mm : MFD of 1.2 meter
- 100mm macro : MFD of 30 cm
- 17-55mm : MFD of 35 cm
On a fixed lens camera (such as the G3X), the "macro" mode (for a lens) is usually there to tell the camera that you want to use a reduced focus range (or working range) so the camera will focus faster on close objects. In this case, the range of distances at which the camera can ask the lens to focus on will change from [MFD - infinity] to [MFD - X meters].
On the Canon 70-200, a similar option is possible using a switch, only this time it will restrain the working range from [MFD - infinity] to [X - infinity] (with X > MFD), again to decrease focusing time. As the 70-200 is a "sport" lens and not a "macro" one, its main purpose is to be used on subjects further away.
Now back to your question
If your camera has the same "normal FR" and "macro FR" then it means that the "macro mode" will not restrict the focusing range of your camera. It will try first to focus in the ([MFD - X] range (close objects) and if it fails, then it will try the [X - infinity] range.
A note on macro (disgression)
Usually, no "maximum focus distance" is mentioned by the lens manufacturer because it's infinity (related : What is "infinity focus"?). Given that, you can focus on every object between MFD and infinity. In your case, you are correct when saying that you can in theory focus on everything in the [30cm ; infinity] range.
Below MFD, your camera won't be able to focus (the internal element of your lens moving to adjust focus will reach an extreme position). It will try and fail to focus, stop bothering and the image will just be blurry (sorry, no monster are going to pop-up form another dimension).
In certain case (only for macro application as far as I know), the use of additional element on the lens can reduce "infinity" to a finite value, for example with extension tube (look at What are the biggest differences between Reversal Rings, Extension Tubes and Macro Lenses? and What am I losing when using extension tubes instead of a macro lens?).