Including Canon Log 2 would not increase the dynamic range of the camera. The color profile just maps the available DR in a pre-defined way.
Canon Log 2 is best used with the raw codecs offered here anyway, and since this camera can record raw, both internally and externally, you can apply Canon Log 2 to the raw files in your coloring software like DaVinci or Final Cut Pro X (and others), if you like.
What you can't do, is bake Canon Log 2 into non raw files internally. But for non raw codecs, I'd say Canon Log 3 is the better option anyway.