First, a clarification- I connect all of my calls on my iPhone, through my iOS application, i.e. I never use headphones on my computer to connect.
In order to connect my call, I do one of three things.
(1) go to google.com/voice, and enter the number. It calls me back on my iPhone, and I talk.
(2) use the dialer in the iOS app.
(3) click on the name in the iOS app.
After the call is through, I see a dialed number in the screen that has a list of all of the numbers I've previously dialed, or that have dialed me. If I click on the number that I dialed, instead of re-dialing that number, it filters all of the calls I've made to that particular number. In the upper right, there are three dots. If I hold on that, the following screen comes up.free USA Voip calls with searchable contact list
From there, it creates an iOS contact. Not exactly one touch now that I'm going through it... but close enough that it seems so. But again, this is specifically on the iOS, so your experience might be different.