No, it’s not possible. You would need to create your own font file using IcoMoon. Font Icons are just a font, so you can create them like a regular font and include them on your site using @font-face.
When you first introduced the essential icons only option in an update my social icons fell over. I only have five Twitter, Facebook, Google, Pintrest and Reddit.
Which of those is not included in your stable of essential icons?