Please correct me if I'm wrong on either of these points.
Assumption 1 - using the international emergency number 112 will force the phone to connect to any available network to make an emergency call. 111 won't as it's not an internationally recognised emergency number.
Assumption 2 - all W850 phones can also operate on the GSM frequencies used by Vodafone's network (just not their W900 3G network).
Would it not be better for us to use 112, as that would provide a backup option if one network were unavailable?