Does an apple watch with family set up (for an elder who lives in a different state) require the paired phone to be nearby for any reason?

I understand that with family setup, I must pair and configure the apple watch for a family member (in this case, my elderly mother who lives in another state) with an iphone. She has no use for her own iphone, and refuses to carry it around, but the watch is small enough that she is willing - so family setup makes more sense.

If I do so with my phone while I am visiting, but then take the paired phone away with me, will there be a point where my phone is necessary for her watch to work? Can I change settings remotely, download updates etc, or do they have to be on the same wifi network to do so? How likely is it that it would stop functioning for any reason without the paired phone available?