Yes, it is possible.

Using the example from this post to create hooks, let's read a secret and pass it as environment variable to the container, to later read it in the postStart hook.

--- 
apiVersion: apps/v1beta1
kind: Deployment
metadata: 
  name: loap
spec: 
  replicas: 1
  template: 
    metadata: 
      labels: 
        app: loap
    spec: 
      containers: 
        - 
          command: 
            - sh
            - "-c"
            - "echo $(date +%s): START >> /loap/timing; sleep 10; echo $(date +%s): END >> /loap/timing;"
          image: busybox
          env:
          - name: SECRET_THING
            valueFrom:
              secretKeyRef:
                name: supersecret
                key: password
          lifecycle: 
            postStart: 
              exec: 
                command: 
                  - sh
                  - "-c"
                  - "echo ${SECRET_THING} $(date +%s): POST-START >> /loap/timing"
            preStop: 
              exec: 
                command: 
                  - sh
                  - "-c"
                  - "echo $(date +%s): PRE-HOOK >> /loap/timing"
          livenessProbe: 
            exec: 
              command: 
                - sh
                - "-c"
                - "echo $(date +%s): LIVENESS >> /loap/timing"
          name: main
          readinessProbe: 
            exec: 
              command: 
                - sh
                - "-c"
                - "echo $(date +%s): READINESS >> /loap/timing"
          volumeMounts: 
            - 
              mountPath: /loap
              name: timing
      initContainers: 
        - 
          command: 
            - sh
            - "-c"
            - "echo $(date +%s): INIT >> /loap/timing"
          image: busybox
          name: init
          volumeMounts: 
            - 
              mountPath: /loap
              name: timing
      volumes: 
        - 
          hostPath: 
            path: /tmp/loap
          name: timing

If you examine the contents of /tmp/loap/timings, you can see the secret being shown

my-secret-password 1515415872: POST-START
1515415873: READINESS
1515415879: LIVENESS
1515415882: END
1515415908: START
my-secret-password 1515415908: POST-START
1515415909: LIVENESS
1515415913: READINESS
1515415918: END