Is there a way to access hard drives while computer sleeps? Is there any way at all possible or possible with hardware (aside from a NAS) to access hard drives while the computer is in a low power mode such as sleep (aside from WOL)?

For example, can I log into a networked drive located on the computer and spin it up to access data without the computer coming out of low power mode?
Sure.  It all depends on the architecture of the machine.  For instance, if there is a co-processor that is awake and responds to the network requests by accessing the hard drive, that would be one way to accomplish it.

If you're asking about a specific product or technology, that is off-topic here.  But conceptually, you can certainly build a computer that has this capability.  Whether any individual computer does have that capability is a question about that specific product or technology.