You have your rig. Take out old HDD drive, SATA cables only will work. Put a new ssd in there. In BIOS select boot-from device CD-ROM. Sometimes you dont need that and the pc automatically asks if you want to start from disc insterted (windows installation). Install windows in the ssd you inserted. When it's installed, in your BIOS find boot-from devices, move ssd to the top or mark as number 1. Re-connect old HDD. Right now you can leave it as it is and it will work perfectly.
Now, the only problem is that your last windows partition is still on that 2TB hard drive and it occupies a lot of space since there will be your old OS and every application and driver you installed. I'm not sure if you will be able to simply delete those by hand. IMO it should be possible, because you will have new OS installed, new administrator rights etc.. and old OS will be just files stored in the old disc. That's just my logic, don't take it as a fact. The easiest way for me would be save what you need into ssd, then format hdd, and copy your files back to hdd. In this case you should be able to save about 400-450GB of data on your ssd. Personally, after windows re-installation i prefer keeping my files neat, that's why i recommend formatting HDD with old files you don't need, but if you're good with what you have, it's not necessary.
Long story short: Yes, once you install SSD with a new copy of windows, you can leave HDD as it is. HDD won’t interfere Windows from SSD (if boot-from device will be set to SSD). But it has a lot of space occupied by OS, system/windows apps, games, drivers installed etc.. If you want to re-gain that storage, i would recommend saving data you need in SSD and wiping up the HDD. Hope you got the answer!