The Soviets never would have fought us militarily, because we would nuke them off the face of the Earth had they tried. So it doesn't really matter how strong their military was, what matters is the fact that they were crumbling economically.
Thomas Friedman, a centrist economist, believes that the Soviets would have fallen even if Reagan hadn't outspent them. When you look at their constant attempts at industrialization, and the negative impacts each phase of their industrialization had on their economy (because no one would trade with them, they wound up spending more on manufactured goods than they took in), the USSR would have crumbled either way. Perhaps Reagan moved up the date they would have collapsed by forcing them to spend more militarily, but there was no way the Soviet Union would have stayed in tact through the end of the century if you solely look at their industrial sector.