It can. Usually when booting up, the computer tests each component, which involves spinning up all disc drives and hard drives. It's normal to hear them then. If a disc drive continues spinning without a disc, then we might have a problem. Hard drives do tend to spin up and down depending on the load.
You could disconnect the disc drive to see if it is the cause of the noise, and otherwise it is likely to be the HDD. Assuming it's not a fan hitting something, or anything like that.