I just tested it on my 2014 box several times and took out the stop and start of the service and the account was changed however, it caused some issues and the Agent will not come online.
This is what I had always gone by
From MSDN.. https://msdn.microsoft.com/en-us/library/ms345578.aspx
When you change the service startup account for the Database Engine and SQL Server Agent, the SQL Server service (the Database Engine) must be restarted for the change to take effect. When the service is restarted, all databases associated with that instance of SQL Server will be unavailable until the service successfully restarts. If you have to change the service startup account of SQL Server or SQL Server Agent, make sure that you do so during regularly scheduled maintenance or when the databases can be taken offline without interrupting daily operations.