iCloud Disassociation for a Mac Computer
I have decided to sell the system. I'd like to know if I remove the
hard drive (or in this case, an after-market SSD I've installed) from
the system, will there be any other data (i.e. iCloud data) stored on
the system on any other chip that I can reset in any way?

Unless you actually wipe the SSD clean, you could potentially leave all sorts of personally identifiable information on that drive. As for &quot;data on a chip,&quot; there's nothing identifiable that stored.  Apple uses your serial number and the MAC address of your network adapter to validate you to their services.  Once you remove it from your account (see below), the hardware is now disassociated from you.

I plan to reset the SMC/NVRAM before I sell the system off of to
someone else.

This does nothing.  This is Internet folk lore that this has an actual function related to macOS.  What these two things do is:

Reset the SMC (Systems Management Controller) is resetting what the rest of the industry calls the PMU (Power Management Unit).  If you're having issues with power, battery, charging, etc.  you would reset this chip

Reset the NVRAM, this doesn't store much - just pre-boot environment variables like where to boot from.  It has nothing to do with iCloud.



Additionally, if I remove the hard drive, is the system still
associated to iCloud (specifically Find My Mac) or any other service?
If so, how do I disassociate it?

Yes.  It's based on the Serial Number of the device.  You can remove it from your account by logging into your AppleID account and removing it.
AppleID
The image below shows how to remove the device from your AppleID account (there's no SN# on that one because it's a VirtualBox VM of macOS Sierra running on my iMac)

iCloud &amp; iTunes
You need to sign out of these as well.  You go into your local settings and sign out of each service respectively.
Apple has an excellent support document What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch

The system will no longer boot even if I put in my boot device.

It will still boot from USB (if the drive is good).  The best way to ensure that it's still good and it is in fact the cable is to hook it up via a USB to SATA adapter.  If it is, you can wipe the drive and install a fresh copy of macOS on it.
(You might want to change out the cable - it's pretty inexpensive - see this link in the comments)