I won't need to reinstall my OS or anything? Or would any other complications occur?
If what you're asking is whether or not you can get rid of your HDD and replace it with another one (or just get rid of it entirely), the answer is yes.
*All* drives are completely independent of one another (Unless you specifically make them not so through RAID for example) and removing one will never affect the other.
If you remove that HDD you will not have to reinstall your OS or anything for that matter. It's an entirely painless process.
Good luck. =)