An individual household that owns stocks will have higher wealth and will want to consume more, just as predicted by the wealth effect. For the economy as a whole, the story is more complicated because the additional aggregate demand is likely to push up interest rates and limit the rise in stock prices.
Both the productivity spurt itself and the induced rise in interest rates will then affect desired investment, international capital flows, and the trade balance. Suppose, instead, that stock prices increase because households are applying a lower discount rate to future profits. Whether an individual household will want to consume more is unclear in this case.