Can host aliases be assigned to deployments in Kubernetes? If so, how?

Yes this is possible. All you need to do is follow the same advice you were for a pod specification, but rather than applying it to a YAML file for pods, you apply it to a YAML file for a deployment. For example, if you are already running a deployment you can edit the current deployment by issuing the following command.

$ kubectl edit deployment DEPLOYMENT_NAME

This will allow you to access edit mode of the currently running deployment in YAML format.

You need to add the 'hostAliases' section in the deployments 'template: spec' field which allows you to configure the template for the pod/containers. So to demonstrate this visually, here is the YAML for a deployment I am running in my project that I can edit by running the command I mentioned above:

apiVersion: extensions/v1beta1
kind: Deployment
metadata:
  annotations:
    deployment.kubernetes.io/revision: "6"
  creationTimestamp: 2018-01-30T14:42:48Z
  generation: 7
  labels:
    app: nginx-site-app
  name: nginx-site
  namespace: default
  resourceVersion: "778922"
  selfLink: /apis/extensions/v1beta1/namespaces/default/deployments/nginx-site
  uid: dc4535333d-05cb-11e8-b5c0-7878748e0178
spec:
  replicas: 1
  selector:
    matchLabels:
      app: nginx-site-app
  strategy:
    rollingUpdate:
      maxSurge: 1
      maxUnavailable: 1
    type: RollingUpdate
  template:
    metadata:
      creationTimestamp: null
      labels:
        app: nginx-site-app
    spec:
      containers:
      - image: gcr.io/myprojectid/tuneup-nginx:latest
        imagePullPolicy: Always
        name: nginx-container
        ports:
        - containerPort: 80
          protocol: TCP
        resources: {}
        terminationMessagePath: /dev/termination-log
        terminationMessagePolicy: File
      dnsPolicy: ClusterFirst
      restartPolicy: Always
      schedulerName: default-scheduler
      securityContext: {}
      terminationGracePeriodSeconds: 30
status:
  availableReplicas: 1
  conditions:
  - lastTransitionTime: 2018-01-30T14:55:28Z
    lastUpdateTime: 2018-01-30T14:55:28Z
    message: Deployment has minimum availability.
    reason: MinimumReplicasAvailable
    status: "True"
    type: Available
  observedGeneration: 7
  readyReplicas: 1
  replicas: 1
  updatedReplicas: 1

If I want to add 'hostAliases' to the pods within this deployment, I need to add this information to the pod template spec section as demonstrated below (notice it is in line with 'containers' (***important- it's worth noting that there are two 'spec' sections within my file- I don't want to add it to the first spec section, but rather the template spec section which defines the pod template):

     spec:
       containers:
       - image: gcr.io/development-project-192309/tuneup-nginx:latest
         imagePullPolicy: Always
         name: nginx-container
         ports:
         - containerPort: 80
           protocol: TCP
       hostAliases:
       - ip: 127.0.0.1
         hostnames:
         - myadded.examplehostname

hostAliases is part of the PodSpec, which is what you also find in Deployment under spec.template.spec in your Deployment so you can easily use it in the same way in your Deployments Pod spec template as you do for Pod it self.