Maybe. Depends on whether the issue is drawing down the battery with the engine off, or whether there is too much load with the engine running.
Might help. But presumably the fans come on when needed, or maybe a little below. I assume this doesn't have some sort of fancy predictive system like sometimes used in HVAC.
I think you can go about this two ways. One is to add up on paper all of the power needs. Then, like Rob just posted, get power output graphs or the info for your alternator. What you want is power at X several rpms (it may be in alternator rpms and you'll have to do the conversion to engine rpm). They might have it in Watts, but more typically it will be amps at some voltage. Then you'll know if all of the power needs at idle can be met by the alternator. All but the battery, that is. The battery recharging after startup should be only temporary, but if the alternator can be able to provide 10 or 15 amps that s probably all the battery can safely handle anyway.
The other approach is to measure the actual current draw of the items and the alternator output after starting etc. These days many multimeters will accept a clamp type ammeter. Sometimes on e-bay an old fashion deflecting type ammeter can be found. They're really only good for higher current cables.
[FOR SALE] - MT-1112 Inductive ammeter set
I have those but generally I use Innova's Current Clamp 3347 with their Automotive Multimeter 334A.
Here's another version
[FOR SALE] - MAC TOOLS EM110 inductive pick up amp clamp
