Could you listen for components props changes?

Yes. You can watch props to execute some code upon props changes:

new Vue({
  el: '#app',
  data: {
    text: 'Hello'
  },
  components: {
    'child' : {
      template: `<p>{{ myprop }}</p>`,
      props: ['myprop'],
      watch: { 
      	myprop: function(newVal, oldVal) { // watch it
          console.log('Prop changed: ', newVal, ' | was: ', oldVal)
        }
      }
    }
  }
});

And in HTML:

<script src="https://unpkg.com/vue/dist/vue.js"></script>

<div id="app">
  <child :myprop="text"></child>
  <button @click="text = 'Another text'">Change text</button>
</div>