From earlier comments and discussions on the forum, it seems that the New Union Treaty is often seens as something of a silver bullet to solve the USSR's problems in the early 1990s. Personally, I suspect that in practice, even if the treaty was signed and implemented, it might have only served to draw out the dissolution of the USSR to a slower process over the decade, not keep the SSRs together in the long term as many seem to envision. The eventual dissolution might have also come about through a later Russian leader seeking to again centralize power in Moscow by undermining the federal structures agreed upon in the Treaty, prompting one or several of the federal states to withdraw/secede from it. This applies especially to Ukraine, the Central Asian states might have been more amenable to stay in a federal structure with Russia, even if Moscow later would have changed the terms to better suit its priorities.
As for a federal USSR turning into a flourishing democracy, I have my doubts. The totalitarian and undemocratic legacy of the Lenin and Stalin periods, and even the echoes of Tsarism, can be still seen in Russia today. In any ATL without PODs prior to the 1990s, reaching the point where the USSR is a flourishing democracy would require a long and uphill struggle. IMO it would also take a honest effort to look at Soviet history without idelogical blinds, to question the very groundwork the USSR was based on, and to address all the repression, terror and atrocities the USSR was involved in and responsible for, a comprehensive process of lustration if you will, to reach a point where democracy in Russia would take root in a deeper sense than just as a facade to show to gullible foreigners.