When adding a Gmail account with 2-step verification enabled to BlueMail, you will first be directed to the authentication screen to enter your username and password. This will be followed by a request for your 6-digit token (for example, from your Google Authenticator App). If you successfully enter the correct credentials for both stages, you will be able to add the account.
Note: 2-Step Verification is applicable only for new or untrusted devices. Since BlueMail is already listed as a Trusted App, the login process will display only the OAuth page.