From my point of view, it pays to be familiar with the "disconnected battery" procedure for your car, i.e. what will happen when the battery is dis- and then re-connected. Things like knowing radio codes, knowing how to get the alarm / immob back to normal, setting the clock (wrong clocks annoy me immensly) and for fancier cars things like re-calibrating power seats and all sorts of fancy things manufacturers think of. That way, when you have to do a battery swap, you know what to expect and how to fix it. Thus, keeping a battery in a car and connected while charging it saves some effort, but it's gonna get disconnected eventually, so you want to know what you're up for.
Re battery drains, the green machine had an old school flashing light (fake alarm) in the console that came on when the car was off. This car also had a new or near-new battery on purchase (alarm bells), but drained it over about 2 weeks. I reluctantly pulled the console out, and found all sorts of suspect wiring, including ignition-on wires connected to always-on wires. Ripped all of that out and it's behaving well now. Nice thing about old mercs is that the original wires, plugs and switchgear are thick and meaty - the new stuff isn't, so it's easy to tell what's what.
The battery later went flat again due to the car not being started for about a month while the dismantled 450 was blocking it in - down to 1.5v! I think the previous issues had also affected its capacity somewhat. My $30 Aldi smart charger wouldn't charge it as it was too low, so I hit it with the old-fashioned charger (just constant 12V) for a few hours, and then it had enough jigglies in it for the smart charger to take over. Took about a day to get it happy. Battery in the car (lazy) but disconnected while charging.
Car has again been running well since, but the battery maxes out at about 12.8V - ideally this would be 13.3 or so.
Lukas