it shouldn't.
"when not in use" you should know includes things that have nothing to do with the drive. opening windows explorer to look at the folders on an SSD, for example, can poll and wake the HDD. Explorer will wake the drives and they will spin up even if you are not accessing it.
that spin up makes noise.
How much storage will you need? the quietest solution would be SSD's with no moving parts.
I would suggest an external solution. something than can be disconnected when not needed, this will be the quietest HDD solution, off. an external can be placed in something else that can quieten it down further. a cardboard box, a drawer in the desk, a closet...
which brings up a NAS drive, a network attached Hard drive that ca be placed in a room on the other side of the house, now that is quiet.