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.
The minimum power supply is dimensioned to allow for USB powered peripherals.
The idle power consumption of such a SBC like Radxa X4 must be significantly below 5 W, probably around 2 to 3 W.
That is still too high for standard AA batteries, but rechargeable batteries should work.
If a long battery life would be needed, it is likely that one can shut down the N100 CPU and wake it up either periodically or on USB activity caused by the RP2040 MCU. That should reduce the average power consumption to fractions of a watt.
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.