Whenever the battery is disconnected and reconnected, the HVAC systems goes into a full recalibration mode. The little plastic gears and their 20+ year old plastic teeth age and become brittle. During the recalibration procedure, the actuators are pushed to their furthest points to find the minimum and maximum sweeps. Flexing old plastic like this is a recipe for disaster. You'll get broken gear teeth, clicking behind the dash and issues with functionality. The 2 main actuators that routinely fail due to this are located way up and behind the dash and often requires the entire dash be removed to replace them. It can be a tight squeeze but it is doable.
This isn't some scare tactic but known information that has been experienced by many of us on the forum. I wish I had known this before disconnecting my battery, as I now have 2 clicking actuators behind the dash. There are a few know-it-alls running around the forum that say this is false merely because it hasn't happened to them. Yet.
Use this information how you'd like. Removing just the fuse for the component you are working on is safer and will not cause the HVAC relearn to happen.