Yes, the effect works the same when driving a 16-ohm speaker from the 8-ohm wiring, or driving an 8 ohm speaker from the 4-ohm wiring, or driving a 4-ohm speaker from the 2-ohm wiring.
These are the main effects. There will be some minor changes in the extreme frequency response of the output transformer. I'd have to run the design calculations to be sure, but in general there will be more extended highs and less extended bass. I doubt either would be audible. The vagaries of speaker impedance in the deepest bass and highest treble are probably bigger than these effects.
Incidentally, many transformers have (slightly) inferior response at the lower impedance taps. That's not the case with the OT-2 or the OT-5 used in the Kaiju and the MonAmour. That's the reason these transformers don't have simple impedance taps but require re-wiring to change the load impedance.
