Yes and no. You can use their Messages web client, but it's still going to be SMS to and from your phone. It's a contrived and pretty ugly solution IMO.
Good grief. It seems like they are doing everything possible to not make something as good as Apple Messages. Data chat without a phone number, interoperability with conventional SMS and the ability to start an instant FaceTime. And with Group FaceTime, it’s even more compelling. You can even do audio only or start a real phone call or send a video or audio message, all in one place. Other than org politics, I can’t understand why Google messaging services are a convoluted mess. I need a flowchart just to understand it all.