It It depends on what your definition of "work" is.

if you're geo-diverse, and you want writes to happen are more than one place (as in the top nodes at each geographic location can all process requests), then you have to go the traditional consensus route. One server in one region makes a write, and the other servers in the region need to acknowledge the write before they move on, lest state become inconsistent. Pretty sure there's no way around it.

if you're geo-diverse, but are OK with possibly stale reads from time to time, and only writing to one geographic area (server), then it seems possible -- you'd just apply these same principles across a bigger scale rather than same-datacenter. You'd probably also lose a lot of the latency gains though.

Probably not. It depends on guaranteed in-order packet arrival. In general the Internet very much does not guarantee that, so you would need control over all of the networks involved.

Of course you can always tunnel over TCP (you need to tunnel over something, because you can't route multicast over the Internet either), but that would almost certainly eliminate the performance benefits.

I'm in agreement with the other replies here - this seems more useful within a datacenter (and any unit smaller than that, such as an AWS Availability Zone) and not so much useful over the general internet. Too much unpredictability in how things get routed, what types of routers are hit, etc.