I have a Cadex battery analyzer at work that's a real fancy version of that. As long as you can set the right low voltage cutout, it should work for any kind of battery.
I also use a cheap 12v to 120v inverter for testing 12v sla batteries. The inverter has a built in cutout that stops it when the voltage gets down to around 10.5v. What I still don't have for it is a 120v mechanical clock that I could set to 12:00 and start the discharge, then walk away; come back later after it's tripped and see how long it ran. I plug in a 120 light bulb as a load.
"One test is worth a thousand opinions"