It's impossible to know, and I'm an institutionalist, so my bias comes from that POV, but I don't think it would have mattered. The problem with the USSR had more to do with corrupt and ineffective institutions, and that's carried through to the modern day. This treaty, and pretty much any other treaty like it, would just be putting different curtains on the windows. It wouldn't have done anything to fix a court system to make enforceable contracts, or to protect people from the government, or to make the incentives for public employees to not be corrupt, or to make businesses competitive in the world markets. Also, as countries like the Baltic states and Poland improved their economies, the failure would have been more apparent and created resentment. I think it would have just delayed Ukrainian independence for a little while, but that's probably it.

FYI, alternate history and anything less than 20 years ago aren't "history" (see Rules 3 and 5 of the subreddit). You're definitely not adhering to the former and most of the discussion of long-term consequences would violate the latter.

That being said, for the New Union Treaty to have had a chance and not just be another dying gasp of the USSR, it would have needed to at least appear to fix the perceived problems of the USSR: including (but not limited to!) too much central control and the inherent corruption in any centralized power structure. But, those in power liked those "problems" since they were the basis of their power. The fact that 6 of the 15 socialist republics weren't even invited to participate in drafting it, and that opposition to the treaty (among hardliners) focused on how it might let the Baltic states and Ukraine be too independent, says to me that the same forces that led to the anti-treaty coup would have torn the government apart from the inside, probably relatively quickly (like the USA almost did a few times in the early years, culminating in the US Civil War, or how bastard feudalism in England inevitably built competing power blocks culminating in the War of the Roses).