Immediately scale up Kubernetes Statefulset/Deployment to full capacity
I don't think so. StatefulSets are designed for safety above all else so the controller operates one pod at a time.
we found the answer hiding deep in the documentation:
https://kubernetes.io/docs/concepts/workloads/controllers/statefulset/#pod-management-policies
Pod Management Policies
In Kubernetes 1.7 and later, StatefulSet allows you to relax its ordering guarantees while preserving its uniqueness and identity guarantees via its .spec.podManagementPolicy field.
OrderedReady Pod Management
OrderedReady pod management is the default for StatefulSets. It implements the behavior described above.
Parallel Pod Management
Parallel pod management tells the StatefulSet controller to launch or terminate all Pods in parallel, and to not wait for Pods to become Running and Ready or completely terminated prior to launching or terminating another Pod. This option only affects the behavior for scaling operations. Updates are not affected.