Hello there, @fbonomo.

I'm here to ensure that this two-step verification issue gets sorted out so you can log in to your account successfully.

Yes, the  two-step verification will work when using your Google login. You'll be able to sign in to your QuickBooks Online through your Google account once it has been integrated. Make sure that the two-step verification with Google Authenticator was turned on. 

To do that:

1. Sign into your Intuit Account and enable two-step verification if you haven't already done so, learn how to turn on two-step verification.
2. Select Security and then click Edit next to Two-step verification.
3. Click Turn on Authenticator app and follow the onscreen instructions.

Know that you have to use the Authenticator app to create your verification codes. Get the iPhone version at the App Store or the Android version through Google Play. Google Authenticator isn't available for Windows phones.

To disable Google Authenticator, simply disable the two-step verification feature.

However, if you're using the Authenticator and the problem continues. I recommend contacting our Customer Care Team. They have the necessary tools that can help identify the root cause of this issue.

To reach them:

1. Click on Help at the top menu bar.
2. Hit on the Contact Us button.
3. Enter a brief description of the issue in the What can we help you with? box.
4. Press on Let's talk.
5. Select on Get a callback.
6. Key in your contact details, then tap on Confirm my call.

Lastly, you can always read through this link, which contains details on how the two-step verification feature work in QBO: Learn how to set up or disable two-step verification for your Intuit account.

Keep me posted if you have questions. I'll be around to answer them. Have a great day ahead.