Yes, you can. Echo Speaks supports Ecobee devices with embedded Alexa. Here's the thread:
Echo Speaks was originally designed to use Heroku's free hosting service for managing cookies on behalf of Echo Speaks. Heroku got rid of its free service a couple months ago. There are three alternatives to cookie management:
- Pay Heroku $14 a month
- Install it on an rPi (node.js)
- Install it in a Docker container on anything running a Docker instance (rPi or wherever you like to dock your Docker)
I use the rPi non-docker version and it works great.