I would say probably not, or at least not for a long time. After spending a lot of time looking up info on these smart speakers Amazon and Google seem to be taking two different approaches.
Amazon is going for the home control/smart home functionality segment as evident by the number of skills are available on the platform and multitude of items that can be controlled by the Echo. They really want to make it a smart home hub, plus integrate it with other Amazon service like Amazon Music and Audible.
Google is more after the personal assistant aspect, which is why I’m thinking they didn’t give it a human sounding name, just Google Assistant. Calendars, reminders, news/sports run downs, asking questions and having it pull from their own search results. Plus data mining. Google is all about data mining.
Not saying that there isn’t a lot of overlap between the two, or Amazon is terrible with providing data and Google is terrible at home control, it just seems like at this time, that is where each company is going with their platform.