You can do exactly that, but it won't work!
With Windows installed on your SSD, the operating system's Registry is also written on the SSD. Most programs you install, also write entries into the Registry regardless of whether you install them on the SSD or the HDD. The Registry is what tells every program installed on your computer how to run and where it's necessary files are located.
When you perform a clean install of the operating system on the SSD, the registry gets re-written and all your previously installed programs have no idea how to find all the files it needs to run. Therefore, they too need to be reinstalled and their registry entries re-created.
-Wolf sends