To answer the OP.
I have used a switching power supply to charge a lead acid battery.
A little background: A couple of years ago I designed the electronics for a “multipowered” refrigerator. Here’s a link to it ‘case you’re interested:
But let me tell you something: It wasn’t easy.
The first thing I needed was a charge controller. I chose to use a commercial unit. The charge controller basically senses the battery voltage and passes current to it via a series MOSFET using pulse width modulation. (Nice, efficient technique.) The duty cycle depends on the battery voltage. I adjusted the control voltage to 13.2V.
I next needed a power supply. The specs called for 120/240 AC input over a fairly wide frequency range, so I had to use a switched-mode power supply.
So I purchased a run-of-the-mill 100 watt, 15VDC switching power supply, hooked up the charge controller & lead acid battery, and proceeded to blow up the power supply. I tried a couple other power supplies and they blew up, too. (I didn’t want to use an external current limiter for various reasons.)
Why did they blow up? Well, when you’re charging a battery from a power supply, the battery voltage “rules.” In other words, when the MOSFET in the charge controller was in the “on” state, the battery was basically connected directly to the output of the power supply. So now there’s a battle going on: The power supply vs. the battery. The power supply wants to be at 15 V, and the battery is at a voltage determined by how much charge it has. So who wins this battle? Answer: The battery.
So what happens to a power supply when you force its output to be something it doesn’t want to be at?
It depends on the output circuitry of the power supply, in particular how it “deals” with an overload condition. (I found this out the hard way.)
You see, when a regulated power supply is adjusted for 15 V, and you hook a beefy lead acid battery to it that is at (for example) 11 V, you basically have an overload/overcurrent from the power supply’s point of view. So how does the power supply handle this? Most (good) linear supplies go into “constant current” mode when you do this. In other words, most linear supplies will “drop their voltage” (i.e. limit the current) to match the battery’s voltage and deliver the maximum current that it is capable of delivering. This is a good thing.
Switching supplies don’t tend to do this, simply because they’re usually never asked to do this. They tend to either shutdown or blow up.
So what I needed was a switching supply that behaved like a linear supply.
I spent weeks calling every power supply manufacturer and distributor in the U.S. to ask if they had a switching power supply that would not blow up or shutdown in overload/overcurrent condition. Only one manufacturer said that their switching power supplies “behaved like linear supplies when in overload/overcurrent condition.” I responded, “Oh yea? Well I’m going to hook one up to a lead acid battery. How do you like that! So are you certain your power supply won’t fry when I do this?” They said, “We’re certain. We’ll even guarantee it.”
And they were right; their switching power supply worked perfectly when charging a lead acid battery.
Moral of the story: You can use a switching power supply to directly charge a battery, provided you have the right kind of supply and the right kind of charge controller. But is your computer’s power supply the right kind? I wouldn’t bet on it.