I know that Three have an arrangement to roam onto Vodafone, so there is
obviously some commonality between GSM and 3G.

Whilst I understand that there would be very few geographical areas
where this would happen due to coverage of the other networks, if you
were in an area where there was no coverage from Telstra, Optus or
Vodafone, but there was coverage from Three, would a GSM handset be able
to talk to Three's network and have it carry a 112 call?