You have the same advantages and disadvantages with static-linking in general. If you want an easily distributable application (non-enterprise), then I think something like this is a great middle ground.

The biggest attack surface for Java is from the web, so that should limit the disadvantages of embedding a JVM. So long as you aren't using your embedded JVM to load external code, you should be okay.

The difference between this being that normally you're only linking specific libraries that you need, instead of an entire runtime and standard library. There's a lot of potential energy hiding in each of these packages.