Is it possible to provision nodes with instance store on EKS with Karpenter?

It's absolutely possible, as long as there is a Provisioner that does not restrict the instance types to those without instance storage.

There are a couple of ways to go about provisioning nodes with instance storage. One is to have Karpenter always launch nodes with instance storage, by specifying that instance types in the Provisioner, such as:

apiVersion: karpenter.sh/v1alpha5
kind: Provisioner
metadata:
  name: instance-store
spec:
  requirements:
  - key: karpenter.k8s.aws/instance-family
    operator: In
    values: ["c6gd", "c7gd"]

The other is to create a Provisioner that has no requirements (or at least does not exclude instance families with an instance store) and to specify the instance type or family in the Pod spec:

apiVersion: v1
kind: Pod
metadata:
  name: with-instance-store
spec:
  affinity:
    nodeAffinity:
      requiredDuringSchedulingIgnoredDuringExecution:
        nodeSelectorTerms:
        - matchExpressions:
          - key: karpenter.k8s.aws/instance-family
            operator: In
            values: ["c6gd", "c7gd"]