The short answer is, yes!
For local web pages, these can be added directly. You will get an error when adding this as an asset in Screenly, because we are not able to access or verify any non-public assets. However, you can just click 'Add Anyway', and proceed as normal.
For local images, these work a bit differently. These are not currently officially supported and cannot be added directly. For these, though, there is a workaround that can be used if you are able to host local web pages (local web server). Here is how that works.
Let's say you have a local image you want to display with this URL: http://10.10.1.1:8081/local/myimages/welcomescreen.jpg
You will want to use the following script below, and save this as an HTML file in the same directory/folder as the image.
<body style="background-image: url(http://10.10.1.1:8081/local/myimages/welcomescreen.jpg); background-size: contain; background-repeat: no-repeat; margin: 0; background-position: center; width: 100%; height: 100%; background-color: black"></body>
Once done, you will add the new HTML asset to Screenly, for example http://10.10.1.1:8081/local/myimages/welcomescreen.html