Yes, hybrid drives work by storing pretty much all of the data on the magnetic disk while using the SSD portion to cache commonly used data so you can access it much quicker than if you were to get it directly from the magnetic disk. On most hybrid drives this is done by the firmware on disk at a base level and doesn't involve the OS or drivers in any way at all.

To expand on this answer further, the root partition on my current Linux machine is at 7.62GBs which is lower than the SSD cache so it would be a fair conclusion that most of the data on the root partition would be copied to the SSD side of the drive as root data is essential for Ubuntu to operate and would be used most if not all the time.