Update (2016-03-19)
Not yet, but Edge decided to support roughly the same WebExtensions model as Firefox - partial compatibility with Chrome extensions. They will be offered through the Windows Store.
Edge began deploying experimental extension support. This is currently in Insider Preview builds and an extremely closed beta preview of the platform. See Also Updated Frequently Asked Questions .
Some variations of Twitter quotes from developers:
Jacob Rossi when migrating extensions
Many questions on this: yes, we are working on a porting tool to run Chrome extensions in Edge. Not yet completed, and not all supported APIs
Jacob Rossi on developer accessibility storage
The store extn will first be a carefully selected set covering the top scripts and API coverage, opening up more in the future
Kyle Pflug when loading non-carbonated extensions
We will allow loading on the sides after starting, but this will require the dev mode switching mode and will have corresponding warnings in the user interface