The thing that causes battery failure is sulfer compound bridging of the plates, causing shorting, and that’s caused by leaving the battery in a discharged condition. The more it’s discharged, the more sulfation and the shorter the battery life. The key to battery life is keeping the battery as fully charged as possible at all times, and the best way to do that is keep the battery on a float charger at all times.
Parasitic draw only hurts a battery if it discharges it enough to allow sulfation. The degree to which it does that depends on the amount of draw and the time over which it occurs, but all batteries have some degree of sulfation and therefore some degree of self-discharge. It may be insignificant at first, but over time it will progressively kill the battery. Leaving a battery, AGM or otherwise, continually hooked up to the battery charger (with power on) is the best way to prevent sulfation, therefore keep it healthy
Some chargers have a mode that supposedly reverses sulfation. I don’t know if those help much, or at all. I suspect that if the sulfation is light, it would be helpful.
I religiously plug my airplane in to both an Odyssey battery charger and a dehydrator as soon as I roll it back into the hangar. I don’t know if the dehydrator helps, but I have a LOT of seasonal rolling stock around here that spends their entire off-season on a float charger (cars, boats, motorcycles, snowmobiles, etc) and it’s a very rare thing that I ever have to replace a battery on any of them.
I agree that a battery charger shouldn’t be left on a battery unattended, unless it’s a “float” type charger (Battery Tender, Battery Minder, etc) that senses the rate of charge and shuts down when charged, comes back on with any discharge. Those are designed to be used 24-7 unattended and are safe and won’t overcharge and boil off the electrolytte like a regular charger can. As to running electronics….I don’t know. Theoretically, the mfrs say that it can harm electronics. I know that the previous owner of my airplane ran the electronics for years while on a plain old Battery Tender without damage. However, I did recently get a 13.7v 30-amp power supply from Amazon and now I disconnect the float charger and plug in the power supply if I’m going to run the panel on the ground.