When you say without service, do you mean she just does not have an cellular telephone service set up with a carrier, or there is no cellular signal where she is? In the USA, all carriers must support and allow 911 calls on their cellular networks even if the handset has no associated carrier or service established. So as long as she has a cellular tower within range, then yes, the SOS feature 911 call should go through (oh, and of course, make sure she does not have airplane mode on and just wifi enabled).
Without cellular telephone voice service with SMS enabled on the account with the carrier, she cannot send texts at all. Her iPhone would be restircted to iMessage only, which of course is an internet messaging service and only works between Apple devices.
SMS messaging is only possible if you have an SMS messaging plan and service with a cellular telephone service provider. SMS texts are sent over the cellular telephone voice channel, and do not use either cellular data or any internet connection at all. MMS uses cellular voice bandwidth for the text portion, and cellular data for the data portion.
Even though Google Voice has an instant messaging service with it, that is not a native SMS service and is handled by Google's hardware, so the SOS function and the iOS messaging app cannot send or receive Google Voice texts.
So, bottom line is that without cellular service, the 911 call part of SOS should work as long as the device is within range of a cellular telephone tower. But without cellular service, the SOS texting function won't work at all.
Use Emergency SOS on your iPhone - Apple Support
