Your Fat Boy has a well made chromoly frame with decent parts on it. From that perspective, I'd say it's worth the time and effort needed to bring it back to rideable condition.
Your bike is also in decent condition. It doesn't look like anything has been abused, broken, or 'maintained' with a hammer.
If you replace all the consumables (tires, tubes, brake pads, brake cable, and grips), disassemble and clean everything, and repack all the bearings, it looks like it would be a blast to ride.
In my case, I would also put on a new chain and freewheel as a safety measure. It's cheaper than an emergency visit to the dentist.