Yes this should work, depending on your requirements, you could use the "NetworkService" account; but this may not be best practice in your environment.
Here is the TSQL to implement (Replace AdventureWorks with your Database name)
USE [AdventureWorks]
GO
CREATE USER [NT AUTHORITY\NETWORK SERVICE] FOR LOGIN [NT AUTHORITY\NETWORK SERVICE]
GO
USE [AdventureWorks]
GO
EXEC sp_addrolemember N'db_datawriter', N'NT AUTHORITY\NETWORK SERVICE'
GO
USE [AdventureWorks]
GO
EXEC sp_addrolemember N'db_datareader', N'NT AUTHORITY\NETWORK SERVICE'
GO
Note this will give the account read and write permission; but no permission to execute sprocs , I would recommend creating a Database role and granting the execute right to all sprocs then assigning the database user to the role.
More info: http://vyaskn.tripod.com/sql_server_security_best_practices.htm