You can use Web Components inside Cycle.js apps. I've done that in a project and it's running well in production. That's the promise of WCs: they should just work, like other normal HTML elements.
On the other hand, there is wrapping Cycle.js apps as WCs so you can use them in other frameworks. I made a simple library for this: https://github.com/staltz/cycle-custom-elementify/ which is still experimental, and if we have enough time we will try to improve that approach, together with the core team in Cycle.js.