For my part, since I've been playing with the new battery pack in my HP-97, I'm not so skeptical . . .
I've been running the batteries down periodically for a full reccharge, and to do this I run a fun little idle loop. As the power falls, the "low power" LED comes on gradually.
I noticed that, early on, the low power indicator flashes in synch with whatever the display happens to be doing, until the power reaches a greater degree of lowity ( ;^) er, rather, a lower level) at which fuzzy point it stays on continuously.
This indicates that, during that transition period, the power drain of the display is enough to take the voltage below some threshold, and when the display blanks, the voltage is restored somewhat.
Unless I'm missing something, the LED display must be a significant (if not the dominant) portion of a classic's / woodstock's / spice's power usage. (That is, as opposed to the digital circuitry, and aside from the card reader and printer.)