Route testing with Tornado
No, it is not currently possible to test this in Tornado via any public interface (as of Tornado version 4.3). 
It's straightforward to avoid spinning up a server, although it requires a nontrivial amount of code: the interface between HTTPServer and Application is well-defined and documented. The trickier part is the other side: there is no supported way to determine which handler will be invoked before that handler is invoked. 
I generally recommend testing routing via end-to-end tests for this reason. You could also store your URL route list before passing it into Tornado, and do your tests against that - the internal logic of "take the first regex match" is pretty easy to replicate.
I'm new to Tornado, and working on a project that involves some rather complex routing. In most of the other frameworks I've used I've been able to isolate routing for testing, without spinning up a server or doing anything terribly complex. I'd prefer to use pytest as my testing framework, but I'm not sure it matters.
Is there a way to, say, create my project's instance of tornado.web.Application, and pass it arbitrary paths and assert which RequestHandler will be invoked based on that path?