to supress the (harmfull) current transients a boost converter *may* help (at a cost).
A boost converter with an energy accumulator (capacitor) in it would
definitely help, but:
a) The batteriser doesn't have one.
b) People who design battery-powered gadgets know about this problem. Bypass capacitors are EE 101. If you bought a gadget that suddenly shuts down, turns back on perfectly, suddenly shut down again after 2 minutes use... etc., you'd take it back to the shop as faulty. There would be a recall.
The batteriser response claimed that it would be a0 "rectangular block" with the 1.6V flat top. this is not the case. I think they are mixing input and output voltage over const current.
It
is the case for a very specific class of devices (constant current). OTOH:
a) That class of devices is a bad choice for use with a Batteriser. Boosting the input voltage means they use more power, overall battery life will be shorter with Batteriser than without it.
b) None of the devices shown in Batteriser videos so far are constant current - that argument is just there to mislead people into thinking it applies to more gadgets than it really does.