Nothing happens automatically unless you make it happen. Your partition will not auto-grow but if you were
using lvm you could make it grow.
In your case I would recommend adding a new disk and turn that disk into an LVM volume within a volume group. Migrate your /dev/sdj data to the new LVM disk. Format and turn /dev/sdj into a volume and add it to the volume group. Extend your LVM volume using the newly created volume (formerly /dev/sdj). You could refer to the blog article I linked a few sentences ago.
There are other ways around this as well such as using a distributed filesystem like
Hadoop,
Gluster, or something more local such as
greyhole. If you can budget it I would go with Gluster because you can add/remove disks all you want dynamically and you can rebalance the share. Those are more network shares but can just as easily be mounted to a local drive on the system.
Again any of those solutions I recommended for you require manual maintenance of expanding the filesystem or storage pool. Stuff doesn't just happen automatically because there are so many possible configurations for storage that it is up to you to decide what you want and not up to the packagers to make decisions which would likely be poor in many setups.
Edit: I misunderstood the original question. As byannoni pointed out mounted drives won't affect the root partition or any partitions it is mounted within.