In short - Yes!
But perhaps you can have both web servers running at all times. In fact, it'll be less of a load on your hardware.
1st Server - Application Server - runs at yoursite.com 2nd Server - SpookyJs/Test Server - runs at tests.yoursite.com
After the servers are up and running the next thing I'd do is wrap the SpookyJs application with a simple restful interface/api. To start tests and to respond with the result of a test.
An important thing to note here is that when you start the SpookyJS application, let stay open. So that every request to the SpookyJS application (through your interface) calls the "open" or the "then" method.
Again, this is to remedy the issue of spawning too many headless browsers.
After the request goes through, go ahead and respond to the request with the result that spooky gives you.
Maybe that helps?
We are doing similar things with Zombie js... so maybe it will help you (: