Will html image paths still work after precompile?

I'm building a Rails app, but I'm using a plugin in which I have to render my images using only html.

Since I haven't deployed yet, all my images are in RAILS_ROOT/app/assets/images/, so to render an image I have to write the following code:

<img src="/assets/image.jpg">

But when I'm ready to deploy to the web and I perform a precompile, all my images are supposedly going to be moved to my public folder. Will the html still work to link to the image, or will I have to change to link to a different path?

The plugin I'm using is Typeahead:

application.html.erb*

  <script type="text/javascript">
      //....
      $('#typeahead').typeahead(null, {
        maxLength: 5,
        displayKey: function(thing) {
          return "<div  class='typeahead'><img src='" + thing.image_url + "'></div>";
        },
        source: bloodhound.ttAdapter(),
      });
  </script>

things_controller.rb

def typeahead
  #render json: Thing.where(name: params[:query])
  q = params[:query]
  render json: Thing.where('name LIKE ?', "%#{q}%")
end

*Thing.image_tag is currently set to "/assets/image.jpg", except for each thing it's adjusted with the proper file name.