Deploying a locally trained model is a supported use case; the instructions are essentially the same regardless of where you trained it:
To deploy a model version you'll need:
A TensorFlow SavedModel saved on Google Cloud Storage. You can get a
  model by:
Unfortunately, TensorFlow for Poets does not show how to export a SavedModel (I've filed a feature request to address that). In the meantime, you can write a "converter" script like the following (you could alternatively do this at the end of training instead of saving out graph.pb and reading it back in):
input_graph = 'graph.pb'
saved_model_dir = 'my_model'
with tf.Graph() as graph:
  # Read in the export graph
  with tf.gfile.FastGFile(input_graph, 'rb') as f:
      graph_def = tf.GraphDef()
      graph_def.ParseFromString(f.read())
      tf.import_graph_def(graph_def, name='')
  # CloudML Engine and early versions of TensorFlow Serving do
  # not currently support graphs without variables. Add a
  # prosthetic variable.
  dummy_var = tf.Variable(0)
  # Define SavedModel Signature (inputs and outputs)
  in_image = graph.get_tensor_by_name('DecodeJpeg/contents:0')
  inputs = {'image_bytes': 
tf.saved_model.utils.build_tensor_info(in_image)}
  out_classes = graph.get_tensor_by_name('final_result:0')
  outputs = {'prediction': tf.saved_model.utils.build_tensor_info(out_classes)}
  signature = tf.saved_model.signature_def_utils.build_signature_def(
      inputs=inputs,
      outputs=outputs,
      method_name='tensorflow/serving/predict'
  )
  # Save out the SavedModel.
  b = saved_model_builder.SavedModelBuilder(saved_model_dir)
  b.add_meta_graph_and_variables(sess,
                                 [tf.saved_model.tag_constants.SERVING],
                                 signature_def_map={'predict_images': signature})
  b.save() 
(Untested code based on this codelab and this SO post).
If you want the output to use string labels instead of integer indices, make the following change:
  # Loads label file, strips off carriage return
  label_lines = [line.rstrip() for line 
                 in tf.gfile.GFile("retrained_labels.txt")]
  out_classes = graph.get_tensor_by_name('final_result:0')
  out_labels = tf.gather(label_lines, ot_classes)
  outputs = {'prediction': tf.saved_model.utils.build_tensor_info(out_labels)}