The EB3A has a UPS feature that keeps 600 watt inverter working using the AC wall plug and a small battery backup. By using the Car Charging Cable, plug into my B300, I have over 3000+ watts of battery back-up for the EB3A and a UPS unit too. Great.
Yes, you can definitely use it that way! Do you have your EB3A connected to Grid and from your B300 at the same time? Only connecting your EB3A to your B300 battery via the 12V output means that you can only charge it at around 100W. This means you won’t be able to keep the EB3A charged if you connect more than 100W of load for an extended period of time.
Another side note is that you need a separate way to charge your B300 because you can’t use the EB3A to directly charge it unless you use the T400 or T500 adapter or you use the D050S charge enhancer (using the EB3A’s 12V cigarette lighter output which is going to be very slow) or, through your AC200Max, AC300 or AC500 if you have one.
EB3A is connected to the grid so that I have a UPS unit of 600 watts. There is a sight drain on the B300 from the DC connection being on, so I have it connected to the 500 watt brick that is plug into the wall.