I don't think AA batteries have improved a whole lot over the past 40 years, but power requirements have definitely gone up. The linked SBC needs a 12v/2A power supply minimum. I think the CPU in the Model 100 used something like 1 watt max and even then I recall reading somewhere that it went as far as suspending clock cycles in between key strokes to conserve energy (this may have been something else, I can't find where I read it).

So in my very-much-not-an-expert opinion, I don't think it would be feasible to run a modern computer off of AA batteries, let alone for weeks.