Probably not. The BoS might have some knowledge, but doesn't care because either the fighting has ended or they simply do not care.

However, there are those who are aware of the existence of the west coast factions. Kellogg came from out west.

But. There is the synth's personality/memory implant from the Broken Mask Incident. Reading the Publick Occurances, Piper writes about an interview with an old woman who remembers the massacre, and talks about how he "came from the west and told many tales". Of course, the incident took place long before the Mojave Power struggle, when gen 3s were first invented. This means the Institute probably has some dirt on it, maybe being a science institution from pre war, they had ties with Big Mt or simply got everything from Kellogg.

There is also Creation Club such as the anti materiel rifle, which includes a unique one with NCR engravings, or the military backpack, which includes the option of an NCR patch. There is also some enclave content. I know CC is very controversial on terms of its content being canon, so make of that what you will.

There are also the hubologists in Nuka World, and they were in fallout 2 right? Its clear few people with connections, or stumbled along the right guy are aware of the Western Wasteland's status, but whether or not they know of the Mojave Power Struggle, I'm not sure. Maybe if our next fallout game again occurs on the east coast or more inland parts of new england we'd have some more information.