In terms of linear scaling, Schnorr signatures can help a bit. I've seen estimates as high as 40% reduction in blockchain data, but the truth is that we have no idea what future adoption will look like, or how long it might take. It was the same with Segwit; adoption is voluntary and therefore slow.
Whether scalability improves by 10% or 40%, it's still only a linear improvement. If the network is faced with exponential growth, then the improvement from Schnorr will be a drop in the bucket. What we really need is off-chain solutions that provide exponential scale -- like the Lightning Network. The incentivized privacy benefits of Schnorr are a lot more exciting than the potential scaling benefits.