Working example using Ember.run.later

components.async-image-wrapper.js

import Ember from 'ember';

export default Ember.Component.extend({
  imageLoaded: 'image not yet loaded',
  
  // purely to make sure image loads each time and
  // is not cached for testing
  volatileSrc: Ember.computed('src', function(){
    return this.get('src') + '?cache=' + new Date().toISOString();
  }),
  
  actions: {
    imageLoaded(message) {
      if (!this.isDestroyed) {
        this.set('imageLoaded', message);
      }
    }
  }
});

components.async-image.js

import Ember from 'ember';

export default Ember.Component.extend({
  tagName: 'img',
  attributeBindings: ['src'],
  
  loadImage() {
    let img = new Image();
    img.src = this.get('src');
    
    img.onload = () => {
      Ember.run.later(this, () => {
        this.get('onImageLoad')("image now loaded");
      }, 2000);
    };
  },

  didInsertElement() {
    Ember.run.scheduleOnce('afterRender', this, this.loadImage);
  }
});

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({
});

styles.app.css

body {
  margin: 12px 16px;
  font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif;
  font-size: 12pt;
}

h1, h2 {
  //display: none;
}

templates.application.hbs

<h1>Testing async behaviour</h1>
<h2>Using wait() in integration tests</h2>
<p>I thought that by using a promise or the run loop then the wait helper would pause before checking the assertion, but it only works with run.later and I can't work out why.</p>
{{async-image-wrapper src='http://emberjs.com/images/tomsters/sandiego-zoey.png'}}

templates.components.async-image-wrapper.hbs

{{async-image src=volatileSrc onImageLoad=(action 'imageLoaded')}}
<p id="image-loaded-text">{{imageLoaded}}</p>

tests.helpers.resolver.js

import Resolver from '../../resolver';
import config from '../../config/environment';

const resolver = Resolver.create();

resolver.namespace = {
  modulePrefix: config.modulePrefix,
  podModulePrefix: config.podModulePrefix
};

export default resolver;

tests.integration.components.async-image-wrapper-test.js

import { moduleForComponent, test } from 'ember-qunit';
import wait from 'ember-test-helpers/wait';
import hbs from 'htmlbars-inline-precompile';

moduleForComponent('async-image-wrapper', 'Demonstrates wait()', {
  integration: true
});

test('Passes if using wait', function(assert) {
  assert.expect(1);
  
  this.render(hbs`{{async-image-wrapper src='http://emberjs.com/images/tomsters/sandiego-zoey.png'}}`);
  
  return wait().then( () => {
    assert.equal(this.$('#image-loaded-text').text(), 'image now loaded');
  });
});

tests.test-helper.js

import resolver from './helpers/resolver';
import {
  setResolver
} from 'ember-qunit';

setResolver(resolver);

twiddle.json

{
  "version": "0.10.4",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": true
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "2.6.0",
    "ember-data": "2.6.0",
    "ember-template-compiler": "2.6.0"
  },
  "addons": {}
}