IMO it would. The economy was deeply troubled and the way the Yugoslav state spread money around exacerbated national rivalries. Most of the republics felt they were losing by being part of Yugoslavia. The 1974 constitution meant that these economic problems added to the old national divides created government paralysis and that of course intensified the economic and national problems.
And if the PoD keeping the Cold War going doesn't remove Slobbo, IMO the breakup will be violent. That man was a real villain in my view (not to say that he was the worst villain or that all the villains were on the "Serbian" side - there were some exceedingly nasty characters among the Croatian nationalists, for example, but Slobbo's attempt to reform the system with opportunistic Serbian nationalism was like fixing a gasoline leak with a match).
That said, the Cold War continuing could throw off the timetable by several years.
If the Soviets seem to be doing OK economically, the collapse of Yugoslavia could boost Soviet influence in Eastern Europe, since they'd be able to point at the implosion and say "look, Titoism really doesn't work, take another look at our system". Also, depending on what the West does, the people in power in the satellite states could be frightened into closer cooperation with the Soviets.
And of course, the collapse of a Communist state could also weaken Soviet influence and depending on what the West does, the Soviets could be made to look militarily weak as well.
I suspect that either NATO or the WarPac intervening without the other would risk severe tensions, so we may see no intervention, as the people inside Yugoslavia are sacrificed for peace in the rest of Europe, a UN intervention with troops from neutral states or a joint NATO-WarPac intervention. Needless to say, NATO in this TL would be very different. The interventions in Yugoslavia were a big change in direction for the alliance.
fasquardon