Can I use my EB3A as a battery charger? I would like to charge my 100Ah battery.
No
Notwithstanding, you 100Ah battery, is a what GEL,AGM, LFP? Power stations output AC & DC supply, none of which are battery charging capable.
You can plug in a dedicated battery charger to the AC output of the EB3A, but charging a 1,200+Wh battery (100Ah) from a 268Wh power station won’t get you very far. 
Here is my logic, Using the powerstation, plugged into AC outlet (wall), I could use the DC output of the unit to charge 100 watts to my Dr. Prepare Max battery. Probably 12 hours to charge. The battery has the interface with charge port.
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Here’s my logic - To charge a LFP (or other incl AGM) The charge voltage needs to be higher than the voltage of that battery. The DC output of EB3A is a nominal 12VDC, to see if it reaches 12.8V you would need to check with a multimeter.
Most LFP batteries rest at 13.1 to 13.2V and need a higher voltage to begin charging. As you have access to grid power, a dedicated LFP charger would be a more efficient and positive method to charge your Dr Prepper… :)