Yes it would work, but sure looks like without too much effort they would fit in the box with a bit of rework.
-Turning batteries 90°. probably need to move pump over,
-Adding in front I see several options- Hard to see what might be involved.
Only thing that catches my eye is the water tank pump line, which a simple platform to raise, allow moving back against wall. Still might not be enough in front, but that false wall could be cut and moved out a few inches, keeping existing electrical intact. Need a new top.
But a little more thought, as your using a stool seems building out might be advantageous, in day to day use, especially if it lives there a good deal of the time. A 'since your there' thing but not needed to add the battery. But it looks like moving the whole wall out to get room for battery.3-4"?