There are other people who have done this, but none have embedded the echo inside the enclosure. I think two reasons this might be a bad idea is that the echo microphones 1) shouldn't be vertically against the wall and 2) might be affected by the noise of the motors and being inside another enclosure.

We found a Billy the Bass at a thrift store for just under $3. At first I considered using a Raspberry Pi instead of an Echo, but it presented other problems that I didn't want to have to deal with, such as setting it up, amplifying the audio, and just detecting when the wake word was spoken and stopped (the debug output on the commandline wasn't sufficient). So I took an Echo Dot and tried to shove it in the enclosure, and it looked like it would work. Then I hooked a power supply up to the various motors and made sure I could drive them, and I could. The project was feasible!