I don't think it's true the '68 invasion of Czechoslovakia was the only joint action; I distinctly recall reading that the Polish soldiers involved in that invasion felt it was payback for when Poland had been invaded by coalition troops including Czechs sometime in the 1950s. That earlier intervention might not have been under the label "Warsaw Pact" though.
But I have to agree the odds were against the Soviets inviting, let alone pressuring, their Eastern European "fraternal nations" helping them out in Afghanistan. Early on, the Soviet intervention looked like an easy adventure and no one thought it would turn into an attritional meatgrinder. By the time it did, the "fraternal" regimes would have been very leery of being drawn in, and the Soviet leadership was well aware of how weak their grip on Eastern Europe had gotten, so the appeal of diluting Russian losses by sacrificing some Eastern European troops instead was more than offset by the danger of this being the straw breaking an overburdened and very cranky camel's back.
So, the legalistic arguments upthread have weight mainly because both Moscow and the European regimes would want excuses to leave them out of it.
If Soviet hegemony over Eastern Europe had been stronger I daresay they'd have "persuaded" their "allied" neighbors to "volunteer" to help out the cause of progress and enlightenment in Central Asia, pacts and treaties be damned. There might have been a new treaty, or a simple invocation of socialist solidarity, whatever.
Then again, I'm not aware of Eastern Europeans being much involved in the Korean or Vietnam wars, though Russians certainly were, not just as suppliers of arms but in uniforms on the spot, notably as interceptor pilots. I think I might have read about some East Germans roaming around Laos at some point, but by and large the Russians left their Eastern European allies out of their adventures outside of Europe, I think, even when they were strong.
Afghanistan might have been different because first of all it was on the Soviet border, and second because they were losing. But both those considerations are a double-edged sword too unless the Soviets had had genuine allies in Europe, and while I think the Soviet hegemony was a bit more nuanced than simple conquest, involving supporting native factions that otherwise would not have been able to take or hold power and a certain ambiguity about just how bad it was for the "satellites," as we called them in the West, on the whole it's fair to simplify it to "the Russians were unwelcome conquerors" and it would take a massively different timeline for it to evolve to something more genuinely fraternal.
So I'd think a timeline where Soviet Russians would be tempted to consider inviting in some Czechs or Poles or East Germans would also be one where they could win handily in Afghanistan without this help, because it would involve a stronger and richer, more confident Soviet Union.