I know Apple ID does but last I checked there was a requirement for developer accounts to verify through a device.
Edit: yep, here's the error I get trying to sign on to the Apple Developer Program, after I logged in (which involved getting a code via SMS):
> Your Apple ID currently has two-step verification turned on, but two-factor authentication is required. After you turn on two-factor authentication, signing in to your developer account will require both your password and access to your trusted devices or trusted phone number.
Keep in mind you should have some some backup way to access your account in case the mac dies. Dunno if Apple IDs support recovery codes or something similar or if you'd actually need two apple devices.
I have a recovery key for "2-step verification", not sure if it works the same for "2-factor authentication". It's a 14-character string. I also have 3 security questions.
Edit: yep, here's the error I get trying to sign on to the Apple Developer Program, after I logged in (which involved getting a code via SMS):
> Your Apple ID currently has two-step verification turned on, but two-factor authentication is required. After you turn on two-factor authentication, signing in to your developer account will require both your password and access to your trusted devices or trusted phone number.