Using Docker as a means to distribute and use neuroimaging software is a very forward-thinking thing to do, though Docker's adoption as a scientific tool is still in very early stages, so as Chris said, there isn't much quantitative info available on its usage right now.
As with any tool, like git or GNU Make, it has a learning curve that you'll have to consider, as not many uses in scientific software exist yet. Docker itself has undergone quite a few significant changes just in the recent year or two, including the division between Enterprise and Community editions. These are all good developments, for the most part, but it does mean that the installation procedure for Docker is always being tweaked, which may impact its utility to you as a distribution too.
That said, there's nothing preventing you from releasing your software through more traditional means in addition to Docker. It could be excellent have traditional downloads for the application (or for something like the JAR object, since you mention your project is coded in Java) as well as putting your officially supported Docker Image on something like DockerHub. If your project is hosted on an online repository, it's a trivial addition (in terms of storage) to add a DockerFile to the top directory, once you've made sure it works as intended on your machine.
Whether or not Docker adds a lot of overhead to your pipeline depends on what base image you use. The default image supported by Docker is Alpine Linux, which is very similar to Ubuntu but much smaller in terms of memory used, and there are already many variants on DockerHub that have Java Development Kits and the like included. If you build your Docker distribution on one of those, you should see negligible slowdown execution of your code, since containers are very fast to start/stop and are not fully-fledged virtual machines (technically, they're just a combination of Linux namespaces and cgroups, but that's a different story). Unless something sub-optimal is done in creating the image or DockerFile, you shouldn't notice a significant difference in time executing your code with Docker (except for the initial download and build of the Docker Image) vs. running locally.
Either way, it sounds like a cool project, so best of luck!