Ah, nope.
A local processor in Alexa listens for a particular phrase. Then it's starts streaming audio to remote servers. That is what Google claims, and while I tend to doubt it, it's feasible.
Personally I purged everything Google two years ago, including my email. It took nearly two weeks to find and break all my associations.
I've taken great efforts to remove myself as nearly as possible from at least casual web searches, and have been successful at that.
I moved to ghostery Dawn browser, and only use DuckDuckGo search engine.
I have no illusions that I can't be tracked, but I do all I can to thwart it.
In some bright future maybe laws will prevent such data theft, but I'm not holding my breath.
Like so many things that are upside down in our world today, this will persist as along as the majority of people blithely accept it.
"I don't care because I have nothing to hide". This phrase especially sticks in my craw. I bet they don't walk around naked though!