Is a HDD stuck on boot screen still upgradeable to a SSD?

While I do recommend upgrading to a SSD you also will need to replace the HD SATA cable as that is truly your issue you have now. These cables over time fail! While you could also have a failing drive as well I would start by just replacing the cable.

Here is the needed part MacBook Pro 15" Unibody (Mid 2012) Hard Drive Cable and the guide you’ll need to follow MacBook Pro 15" Unibody Mid 2012 Hard Drive/IR Sensor Cable Replacement. There are some other actions you’ll want to do to help protect the new cable. First you want to place a strip of electricians tape on the uppercase where the cable crosses over to the drive. Protecting it from the rough surface of the aluminum case which abrades it as the drive shifts around. The next issue is the plastic bottom cover catches make sure the one near the optical drive is not broken if it is you’ll want to swap it out with the other. A sharp bang to the bottom cover can press down onto the cable as it crosses over the optical drive . I do recommend placing some foam tape to the sides of the cable to help protecting it from the risk if the cover crushing it.

Now the real hard issue! These cables are not designed to be folded to make the crease to get around the corners. All you do is sendup fatiguing the thin foil wires within the cable. Instead you want to use a BIC pen ink straw which is the ideal radius to help you form the arc within the cable for the corner turns.

You brought up one more issue here Cloning! Don’t do it! You want to setup a OS installer drive following this How to create a bootable macOS Sierra installer drive. Make a full backup of your drive after you replace the cable. Use it to reformat your HDD and reinstall the OS. At the end the installer will ask if you want to migrate your stuff from another mac or TimeMachine backup. This is the better way making sure your files are not damaged and any old files and caches are not copied over.