If you are using the other hard driver frequently, copying and pasting files to it, then there is a potential to have a virus there. For example, if you lived in a two bedroom house and knew that sooner or later, someone was going to place $10,000 in one of them, would you check both rooms or only check one?? So, YES, it should be done on both drives.
If you're feeling safe, then you may want to alternate drives on opposing weeks. If you're not accessing the second drive often, such as with a USB external drive, then why not disconnect it except when needed?
Hope this helps.
When you do a virus scan, trojan scan and spyware scan do you really have to scan your whole computer. With a second hardrive installed it takes about 7 hours each week to do this.