This feature is available in all editions.
Yes. You can create a child project called Spike with its own sprint/iteration schedule below your existing project, and then create the spike sprint in that Spike project. Since it has its own schedule, the velocity reports for the main project will exclude the spike sprint. Note that story estimates, etc. would still roll up to the parent project as a whole in this scenario. If you don't want that, you can create a peer project for your spikes to keep them wholly separate from a reporting standpoint.
To learn more, see Sprint/Iteration Planning.