The sensor normally spans so large dynamic range, that unless there are limitations added to the software, it should be able to pick up the focus even when the contrasty features image is a number of stops dark.
But maybe, just maybe, the camera will also make use of auto-ISO while waiting for the actual photo to be taken.
The significant difference between the two focus modes is that the contrast focus have much more information to work on - but will instead not know how much off the focus is. So it need to change the focus and recompute just to figure out if things seem to be better or worse. The phase sensor can compute (most of the time) how far focus is off and what direction and then tell the lens to do a big focus change at maximum speed.
So in the end, the contrast focus can be seen as more robust, while the phase focus works most of the time and then normally with a great speed advantage.