Hi Ryan,
Thanks for getting in touch!
Yes, you can override any calendar template file by adding it to your theme and making modifications from there, like adding a sidebar widget into the template. Our Themer’s Guide has a thorough overview of how template overrides work.
That said, we are actually working on shortcodes right now that will enable you to embed full calendar views on any page or post. That’s been a huge feature to build, but we’re getting ready to release it in our next major version, 4.3, which should be out in the next month or two. 🙂
Does this help answer your question? Please let me know.
Cheers!
Geoff