yes the sum resistance would change but :
before a little elecnotrics law (ohm law) : the total the current flowing in the circuit is given by the voltage / resistance so the less the R the more A , more R = less A
i wrote a little but to be honest is the first law which controls everythings
and at given voltage is the load that absorb "his current" given by his internal resistance if the voltage reamain the same only the resistance control the current flowing
a BURNT glowplug show infinite resistance because it is interrupted
so the sum of the resistance (glowplug are parallel ) is MORE than normal and the super glow circuit (sensing more resistance) feeds the busbar for a shorter time... even doesn't feed at all as if the glowplug were hot
it could be that a completely burnt glowplug can disables all glowplug system because the glow plug circuit see a bigger resistance as if
glowplug were already hot, infact this system was thought to reduce the current when the glowplug were hot enough
for what i understand :
1 superglow : a faulty glowplug does not cause of burning the Others maybe it not feed at all if the total resistence is similar to 4 hot glowplug
2 classic glow, like "Wilson switch" that off course needs a completely different type of glow plug and only a timer ( or watch

) :
a faulty glow plug does not cause of burning the Others because they are in simple parallel, like the bulbs in your huose.
and by ohm law being the resistance of 3 glowplug in parallel bigger than 4 the total current will be lower
if you want to understand more about super glow and glow system in general there are a lot here on mud ... don't think i don't want to explain but to be honest my English is not the best and here on mud you can find a lot written better/correct
check this
Which plugs should I be running - B, 2B, 3B, H and 2H diesels
read untill the end
but there are Others , search
good luck and keep us informed , who knows ? maybe one day i ll have the same problem !
if we can 'll help you