FYI if you look at the small wall-wart that comes with the ER-X (not the SFP) it is a 12V unit. So yes the ER-X SFP will also work on 12V, or rather 13.8 which is what a "12V" battery actually floats at. And yes it's much more efficient to do it that way, plus you can change the run time just by making the battery(ies) larger.
Where you run into a problem is if you use the PoE out on the ER-X SFP - the devices being powered may not like not seeing 24V, and the current limiting per port is 500ma (there are 1/2 A PTC fuses on each output). But you can also use a 12 to 24.0V boost converter to up the voltage - we do that on many Solar powered sites. But it's not for non-technical folks, in most cases...
Jim