As long as your current computer isn't like so old it use some outdated standard. If the cable going to your current hard drive looks something like this, then, no, you don't need a hard drive.
If it's an older drive, which uses a slower transfer rate (below ATA-100) then your performace will suffer, but the drive should work eather way. you will have to install new drivers for your new devices in the operating system, but you would have to do that (and more) anyways if you had a new drive and wanted to install a fresh OS
I see you have XP (says it under your AV), The specifications for XP are strict enough to lead me to the conclusion that your computer is most likely newer, and which means you most likely have an ATA 100 hard drive, so, yeah, it should work just fine.
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