Can China rebalance growth toward consumption?

No, not really.  Rebalance, yes, but the growth part…not quite.

It’s not an aggregate demand problem where C + I + G is the useful way of thinking of the causal determinants of national income.  So a lower I and a higher C will not leave future Y unchanged, even if the boost in C picks up the slack in the very short run.

China has been growing a lot because it has been investing a lot, and investing relatively well, at least compared to where it had been.  Putting a given amount of yuan toward a well-placed road helps an emerging economy more than does spending that money on a bagel.

Turning more of that investment into consumption will mean a lower growth rate.

China of course can and should rebalance toward more consumption, because their investment has been growing increasingly wasteful.  But that is not a path toward maintaining or restoring a seven percent growth rate.  It is an admission that a seven percent growth rate will never be possible again.