I have seen the results of dodgy neutrals a good few times in various different circumstances - none of them nice. ... Never seen an appliance cause this, but it could happen.
I would guess that the situation is only likely to arise if the N-E fault within the installation (wiring or appliance/equipment) pre-dates the appearance of the high supply neutral resistance ...
... to get (as is being postulated in this case) very high currents flowing from the installation's neutral (from loads) through an N-E fault and a low resistance path to earth (bonded extraneous-c-ps, or perhaps a TN-S earth) requires that the impedance of the faulty supply neutral has a considerably higher impedance than that path through the N-E fault. If the supply neutral had had as high a impedance as that prior to appearance of the N-E fault, I would imagine that the considerable voltage drop in the faulty supply neutral would have already brought that problem to the occupier's attention (dim lights and appliance/equipment malfunction etc.).
For example, I would guess that the neutral impedance would usually have to be at least an ohm or two to create the situation we're postulating - so that, in the OPs case, had that fault been present prior to the NE one, switching on the shower would probably have resulted in a drop of 40V - 100V is the installations L-N voltage - which would surely not have gone unnoticed. Is my thinking reasonable?
Kind Regards, John