That is good for charging and will test cca but im not sure about voltage. To be honest i have never messed with the testing functions on one. It is fully auto so while youre in the 2a auto mode it is working like a trickle charger. Make sure that you have it set in the agm mode too.
If you do have a shorted cell you could be overcharging too and burning off electrolyte while its hooked up, that would make the problem worse. If you run by an autozone or advance auto they will put a load tester on the battery while its installed and can tell you if there is a shorted cell. Sears can do this too but it would probably take longer though if there is an issue you can fet it replaced right there.
If you can I would throw a clamp on type ammeter over the power cable going to your computer to see exactly how much it is drawing while its off. Usually alternator issues show up with other symptoms so I am not convinced but cant rule it out yet either.