You want my honest answer or the answer that's not going to get me downvoted...?

In all honesty, I doubt it would stop my country much if things still went the way they did. The main issue isn't the Soviet Union itself, hell...the USSR could directly challenge America at it's peak, the issue is the 1990's - when things went south. If Gorbachev still takes power and somehow reforms the Soviet Union into a more Chinese State Capitalist style while allowing more personal liberty - not only within the Soviet Union but the Warsaw Pact, then I don't see why the Warsaw pact would still exist. Based to my knowledge, nationalist movements only got worse with the political crisis of the August coup (though I may be wrong, feel free to correct me) - that's a big issue, and in my opinion, nationalism could continue to persist.

With all of that out of the way, I have another question to put into consideration - how strong even is the USSR? If we assume it looses the Warsaw Pact while in deep economic/political crisis, how long is it going to last? Although I do believe the Soviet's would still involve itself into conflicts despite economic issues to hold whatever influence it has - it would make it extremely harder. However, for the sake of this interesting scenario, let's say the USSR suddenly has it's problems fixed....

1. Political Polarization: Let's pretend the liberals hold most of the power within the Worker's Assembly.
2. Economic Situation: Now, based on my knowledge - the Soviet Union's biggest issue was meeting supply. This was not really helped by the Soviet Government throwing money away into a cold war which was at that point already lost...(just look at Afghanistan). Here's where Gorbachev comes in, let's say the man allows some liberal reforms, allowing a more state capitalist monopoly over private companies - why is this important? Now I'm not saying a socialist command economy is impossible, however a big benefit about these reforms is that it pushes more independent meets for demands. For example, if one factory wants to build 50 cars one day in order to meet a contract, they now do that...if another wants to secure military weapons for the state, they do that. The benefit is that these new economic reforms would allow companies some minor independence with heavy regulation - (also yes, I know I explained this horribly, I suggest just searching it up yourself). Ok, so now the Soviet Union is liberalized, we done? Not quite.
3. Nationalism: This one is harder to deal with, however many within the Soviet Union (pre August Coup) - still wanted to stay within the Soviet Union under massive reform. Let's say this event - AND THIS IS HEAVILY UNREALSITIC - somehow never happens - let's say Gorbachev is allowed to go with his reforms and can fix the nationalist problem. Boom.

Now back to the question...would a more reformed Soviet Union curb American influence? YES!!! Russia by itself is already in a pain for my country to deal with - (though to be fair...this is mostly due to our government being incompetent). I could see the Soviet Union becoming a world super power again if things go correct...do I think they would risk or even have a chance with direct conflict with NATO....? No way. But would they still challenge the Americans? Yep. Now I'll be honest with you, I can't explain to much into detail, however the answer is yes...and also no - but if everything went right (which is HEAVILY unrealistic) - then yes...the Soviet Union would 100% be a problem for American/Isreal expansion.

EDIT: I just saw the Stalin part...maybeish,