The northern Caucasus and Switzerland are, aside from theoretical similarities in terrain, completely different in terms of their situation for the formation of such an entity.
Switzerland, as a region, has existed in a roughly confederal form for a good seven centuries, and has a remarkably special series of circumstances surrounding the formation of a singular national identity. It originated as a trade league between some alpine Swiss mountain communities and over time coalesced and expanded, developing as a loose assemblage of polities operating as one unit within a loose assemblage of polities and in the process acquiring a well-established character while retaining a level of granularity and regional autonomy preventing forces such as pan-nationalism from ingraining themselves. Additionally, given that the Swiss Confederacy developed over the centuries with mutual benefit of its member cantons in mind, factors such as economy and cashflow have not been especially prominent either. Religion has been somewhat of a dividing factor (see the Sonderbund War), but this declined with the spread of secularism and active government restructuring to prevent such conflicts.
Contrast this hypothetical Caucasian union, which based on your description is identical or nearly so to the
Mountainous Republic of the Northern Caucasus. Independence is easy enough given that this occurred OTL, but survival is entirely different. There aren't really any powers nearby which are capable of defending such a state from theoretical Russian reconquest in the pre-nuclear era, so one would need for the ASSR to survive somehow and then gain independence in a different (perhaps earlier?) Soviet collapse/disintegration. Even then, national identity remains a very prominent issue as there is little commonality between the myriad communities of this country except fear of Russian reconquest and theoretically Islam, and unlike in Switzerland you don't have nearly 700 years of cooperative traditions to draw stability off of. Developing united economy and infrastructure may help settle ethnic and religious quabbles, but considering that the Caucasus was a relative backwater among the regions of the Russian Empire, itself among the least developed of its (European) neighbors, there is quite a long ways to go.
Overall I'd say you would need the Mountainous ASSR to remain intact and see a lot of development of infrastructure using Soviet resources (theoretically not under Stalin or a similarly genocidal character), then for the USSR to fall before it is liquidated or subdivided. How this would occur is not something I can comment well upon.