Likely not as the game hasn't been technically designed to support that. While some may find this limiting, it also has some benefits in the form of universally comparable and easier sharing of ship designs, fleets and levels. The sharing of ships, fleets, levels etc. is likely going to be through Steam Workshop integration. These user created files can already be shared manually.
One of the initial inspirations for this game was Battleships Forever. I really liked the sandbox mode where you could have different kinds of ships and fleets fight each other. It also had (has?) a nice community in the forums creating beautiful ship and fleet designs, but what frustrated me was total lack of restrictions in the ship editor that led to crazy power creep. Most of the designs from the forum were extremely overpowered against all of the vanilla ships and each other as well to the point that you couldn't have any meaningful battles with them. This was maybe around 2009, and Battlefleet Engineer has evolved to something a bit different, but I still think that the core idea of having a standard set of modules and rules is worthwhile even if it limits creativity and amount of content available for the game.
However, the game is already designed to support some customization such as changing the graphics (sprite textures, particle effects) and most of the UI is actually fully "moddable" due to it being implemented using HTML, JavaScript and CSS that are all editable.
