Is there any benefit to using a voltage booster (such as Batteriser) on "dead" batteries?
"Is there any benefit to using a voltage booster on batteries that are below a device's cutoff/operating voltage?"

Of course there are benefits in that situation: a battery that would otherwise be dead can still be used for some time. But probably not for long, so it is debatable whether this is usefull.

What DJ (IMO correctly) argues is that the Batteroo claims are wildly exaggerated at best, and the use of their device with batteries that are not yet below the cutoff voltage will lead to some additional energy use, so the overall effect might be negative.