Does economic growth overcome scarcity

Yes and No.

Yes:

From the consumer perspective, when the economy growth speeds up, their purchasing power increases, thus they can afford to buy a plentiful amount of goods. During this time of growth consumers are not worried about the store running out of goods because they can't see the limits.

No:

The Faster the economy grows, the faster we deplete our natural resources, thus making the Natural Resources even more scarce over time. The consumer isn't aware of any resource limits, so the only way to communicate to the consumer that the materials needed to manufacture a good is becoming scarce is by raising the price of the good. By raising the price of goods consumers lose purchasing power, thus a lot less goods are allocated per consumer balancing out scarcity and allocation.