The Runtime SDK wasn't built to run in a server context. There are security, performance, and file handling considerations that would probably bite you.
Also worth pointing out that the license terms don't allow it (see here, Footnote 19, which is reference in Developer Tools->ArcGIS Runtime SDK).
However, I don't think the Runtime would buy you anything in this case since, as you point out, there's no API for VRP. I'd just make the REST calls from your own Java code.
Lastly… I don't think this will help you unless you're willing to consider Node JS, and you'd have to extend it to solve VRP, but it could give you an authentication and request framework, so I thought I'd mention it: Perhaps check out ArcGIS REST JS.
Hope that helps!
