Usually, the service provider will set rules for the change of appearance affidavit and tatkal service in the country of your residence. For example, in the USA, the VFS does allow you to renew your passport in Tatkal even if your appearance has changed. You will need to submit this affidavit though as a required document. NOTE that the service provider or Indian embassy may not process your application in Tatkal (emergency) if your appearance has a drastic change and does not match the old picture on your existing passport. A real-life example of a person who got his Passport renewed in the USA with the change of appearance in Tatkal service.