Yes you can add the 2TB HDD to the system, just ensure in the bios that it is set to boot off the SSD. One quick note however, is that you will not be able to run some if not most of the programs off of the HDD, not because you can't run programs off a secondary hard drive, but because they were not installed in this copy of Windows. That means that any program that installs files to the system folders or entries to the registry will not be correctly installed. You can always try running them and seeing what happens but if they fail to run a reinstall of the software will allow them to run from your secondary hard drive with no problem.
If you have enough storage else where, I would suggest moving all of the files off of your secondary...