That's not Authy/Google Authenticator. That's social engineering their way into getting a persons text messages for SMS 2FA.
I'm sure it's more complicated than that in reality, but if you have SMS access, you only need to find one weak link in the chain including iCloud/google, email provider, app provider, etc.
You sure can, but will you then have the requisite TOTP secrets?
Good news is according to apple [0], you can protect your icloud keychain with a six digit code required to move the keychain to a new device.